LIBRARY 

OK  THK 

UNIVERSITY  OF  CALIFORNIA. 


<  ;  i  KT  c  )  K 


Ct).  - 

Accession       w.847u>/<5_        Class 


EXPERIMENTAL  PHYSICS 


BY 


WILLIAM   ABBOTT   STONE,  A.B. 

INSTRUCTOR  IN  PHYSICS  AT  THE  PHILLIPS  EXETER  ACADEMY 


BOSTON,  U.S.A.,  AND  LONDON 
GINN   &   COMPANY,    PUBLISHERS 
CTJe  &tj)enaettm 
1899 


COPYRIGHT,  1897,  BY 
WILLIAM  ABBOTT  STONE 


ALL  RIGHTS  RESERVED 


PREFACE. 


THIS  book  is  the  result  of  an  experience  of  nearly  ten 
years  in  teaching  Experimental  Physics  to  classes  consist- 
ing of  students  who  were  preparing  for  college  and  of 
students  who  were  not  preparing  for  college. 

Most  of  the  experiments  are  quantitative,  some  are 
qualitative.  Qualitative  experiments  serve  to  stimulate 
the  interest  of  the  student,  and  to  prepare  his  mind  for 
a  better  understanding  of  quantitative  experiments.  A 
beginner  in  Physics  should  know  something  about  that 
which  he  is  expected  to  measure  before  he  attempts  to 
measure  it.  This  knowledge  is  readily  acquired  from 
qualitative  experiments. 

To  show  the  aim  of  the  work,  I  have  put  at  the  begin- 
ning of  each  experiment  a  concise  statement,  not  of  the* 
result,  but  of  the  object  of  the  experiment ;  and  at  the 
end  of  each  experiment,  questions  for  the  purpose  of  help- 
ing the  student  unfold  the  result  of  the  experiment  from 
his  record.  The  general  results  of  the  experiments  are 
enforced  by  numerous  examples,  many  of  which  have  been 
drawn  from  Harvard  Examination  Papers.  The  experi- 
ments are  often  stepping-stones,  each  to  the  next. 

The  book  contains  only  two  or  three  experiments  which 
require  students  to  work  in  groups  ;  for  my  experience 


IV  PREFACE. 

has  shown  that  students  get  the  greatest  benefit  from  a 
laboratory  course  in  Physics  by  working  each  for  himself. 

My  purpose  has  been  not  only  to  teach  the  student 
something  about  Physics,  but  also,  as  Physics  yields  itself 
readily  to  this  purpose,  to  teach  him  the  importance  of 
distinguishing  between  facts  and  inferences  from  these 
facts,  to  lead  him  to  weigh  facts  carefully,  and  then  to 
use  his  judgment  impartially  in  drawing  inferences.  The 
teacher  cannot  use  too  much  care  in  impressing  upon  the 
mind  of  the  student  the  limitations  which  he  must  con- 
stantly put  upon  his  statements  and  the  danger  of  mak- 
ing generalizations  from  imperfect  data.  The  student 
should  not  think  that  he  is  discovering  laws  of  nature 
for  himself. 

I  am  under  obligations  to  numerous  authors  and  espe- 
cially to  my  former  teacher,  Dr.  E.  H.  Hall.  Among  many 
friends  to  whom  my  thanks  are  due  are  Professor  G.  A. 
Wentworth  for  his  interest,  encouragement,  and  sugges- 
tions, Professor  J.  A.  Tufts  for  valuable  assistance  in 
reading  both  the  manuscript  and  the  proof  sheets  and  for 
the  great  pains  he  has  taken  in  looking  after  the  English 
of  the  book,  and  Mr.  Frank  Rollins  for  reading  the  proof 
sheets  and  for  valuable  suggestions  about  the  experiments. 

I  shall  be  grateful  for  any  corrections  or  suggestions. 

EXETER,  N.  H.,  February,  1897.  W>  A<  S' 


THE  LABORATORY  AND  THE  APPARATUS. 


THE  laboratory  should  be  a  well-lighted  room,  provided  with  a 
sink,  tables,  and  gas  or  gasoline,  if  experiments  in  heat  are  to  'be 
attempted.  The  room  should  also  contain  cases  or  cupboards,  or  a 
large  closet,  in  which  to  store  the  apparatus  when  not  in  use.  Some 
of  the  more  common  tools  ought  always  to  be  at  hand,  such  as  a 
screw-driver,  a  hammer,  a  saw,  a  vise,  a  gimlet,  a  soldering-iron. 

An  intelligent  carpenter  can  make  many  of  the  pieces  of  apparatus. 
In  Boston,  the  L.  E.  Knott  Apparatus  Company,  16  Ashburton  Place, 
are  prepared  to  furnish  the  apparatus  called  for  in  this  book.  Some 
of  the  apparatus  can  doubtless  be  obtained  from  Walmsley,  Fuller 
&  Co.,  134-136  .Wabash  Avenue,  Chicago ;  Eimer  &  Amend,  205 
Third  Avenue,  New  York;  Queen  &  Co.,  1010  Chestnut  Street, 
Philadelphia. 

A  sufficient  supply  of  apparatus  to  provide  for  a  division  of  twelve 
students  working  at  a  time  will  cost  about  $400.  This  estimate  is 
based  upon  the  fact  that  certain  pieces  of  apparatus,  such  as  balances 
and  air-puinps,  can  be  used  in  common  by  two  or  more  students. 

Some  teachers  may  find  useful  the  following  list,  which  shows  the 
experiments  in  this  book  that  are  similar  to  the  exercises  in  the  revised 
Harvard  list  or  that  are  equivalent  to  them : 

HARVARD  EQUIVALENT  HARVARD  EQUIVALENT 

KXERCISES.  EXPERIMENTS.  EXERCISES.          EXPERIMENTS. 

1.  1,  2,  3.  9.  108. 

2.  7.  13.  109. 

3.  13.  14.  110. 

4.  9.  15.  110. 

5-  6.  17.  88,  89. 

6.  10.  18.  92. 

7.  11,  12.  19.  93. 


VI      THE  LABORATORY  AND  THE  APPARATUS. 


HABVABD 

EQUIVALENT 

HARVARD 

EQUIVALENT 

EXERCISES. 

EXPERIMENTS. 

EXERCISES. 

EXPERIMENTS. 

21. 

95. 

43. 

49. 

22. 

96,  98. 

44. 

51. 

23. 

97. 

45. 

56. 

24. 

100. 

46. 

52. 

25. 

102. 

47. 

72. 

26. 

59,  60. 

48. 

78. 

28. 

61. 

49. 

77. 

29. 

62. 

50. 

129. 

30. 

63,  64,  65. 

51. 

139, 

140,  141. 

31. 

66,  67,  68. 

52. 

142. 

32. 

25. 

53. 

138. 

33. 

28. 

54. 

143. 

35. 

106. 

55. 

144, 

145. 

36. 

112. 

56. 

152, 

153. 

37. 

113. 

57. 

154. 

39. 

36,  37,  38. 

58. 

147, 

148,  149,  150. 

40. 

40. 

59. 

151. 

41. 

41. 

, 

The  experiments  in  the  foregoing  list  are  drawn  largely  from  the  Har- 
vard Pamphlet,  but  in  several  cases  with  modifications.  In  general, 
apparatus  has  been  recommended  like  that  devised  by  Dr.  E.  H.  Hall. 
For  the  discussion  of  the  experiments  valuable  suggestions  have  been 
derived  from  Hall  and  Bergen's  Text-Biok  of  Physics,  Hall's  Lessons  in 
Physics,  and  Worthington's  Physical  Laboratory  Practice. 


EXPERIMENTAL    PHYSICS. 


CHAPTER  I. 

MENSURATION,    HYDROSTATICS,    AND    PNEU- 
MATICS. 

1.  Purpose.     The  purpose  of  this  course  in  physics 
is  to  lead  the  student  to  observe  carefully,  experiment 
intelligently,   record   accurately,    judge   impartially,    and 
infer  justly. 

2.  Directions    for    Note  -  Taking-.     In    a    note -book, 
which  must  be  his  constant  companion  in  the  laboratory, 
the  student  should  keep  a   record   of   the    experiments 
which  he  performs.     This  book  must  contain  the  original 
records  of  the  work  done.     No  records  should  be  made  on 
scraps  of  paper,  to  be  copied  later  into  the  note-book. 
A  blank  book  about  8f  inches  long  by  7  inches  wide,  and 
containing  about  250  pages  of  good  unruled  paper,  suit- 
able for  pen  or  pencil,   is  recommended.     The  binding 
should  be  strong,  with  leather  corners  for  the  covers  and 
a  leather  back.     The  first  leaf  should  be  left  blank  for  the 
name  and  title,  and  the  remaining  pages  numbered  like 
the  pages  of  a  printed  book,  the  even  numbers  on  the  left- 
hand  page,  the  odd  on  the  right. 

_84732 


2  EXPERIMENTAL    PHYSICS. 

The  records  of  the  measurements  and  of  the  obser- 
vations should  be  put  on  the  left-hand  pages,  while  on 
the  right-hand  pages  must  be  put  computations  and 
inferences.  The  notes,  which  may  be  written  either  with 
a  black  lead-pencil  or  in  ink,  should  not  be  altered  after 
they  are  made.  An  obvious  error  may  be  corrected  by 
writing  between  the  lines,  but  the  original  record  should 
not  be  obscured  in  any  way  other  than  by  drawing  a  line 
through  the  erroneous  statement.  At  the  top  of  the  left- 
hand  page  must  be  placed  the  number  and  the  object 
of  the  experiment  with  the  date,  and  also  the  names  of 
the  pieces  of  apparatus  used.  The  notes  must  not  be 
crowded.  It  is  a  good  plan  to  make  illustrative  diagrams 
and  sketches.  Not  more  than  one  experiment  should  be 
recorded  on  a  page. 

As  long  as  the  student  does  not  depart  from  the 
general  rules  laid  down,  he  is  at  liberty  to  follow  any 
system  of  note-taking  that  may  seem  best  to  him.  In 
developing  his  method  of  keeping  notes,  it  is  well  for  him 
to  ask  himself  frequently,  "Will  my  notes  tell  another 
person  just  what  I  have  done  ?  "  Let  the  student  make 
his  notes  concise,  yet  so  clear  that  another  in  reading  the 
record  cannot  fail  to  understand  it. 

3.  Directions  for  Performing-  Experiments.  Before 
beginning  work,  the  student  should  read  with  care  the 
directions  which  accompany  •  the  experiment.  In  these 
directions  attention  will  be  called  to  the  precautions 
which  should  be  taken  in  the  proper  performance  of  the 
experiment.  A  precaution  once  noted  will  be  rarely  men- 
tioned again,  but  should  be  taken  whenever  applicable. 


MENSURATION. 

All  measurements  and  other  necessary  data  must  be 
recorded.  On  the  following  pages,  questions  in  connec- 
tion with  the  experiments  will  be  frequently  asked.  The 
questions  must  not  be  answered  by  a  simple  "  yes "  or 
"  no,"  but  by  a  declarative  sentence.  When  the  question 
is  in  parentheses,  however,  the  student  should  not  record 
the  answer  in  his  note-book,  but  should  be  able,  when 
called  upon,  to  give  it  orally. 

4.  Mensuration.  With  a  meter  stick,  having  inches 
on  one  side,  measure  the  length,  breadth,  and  thickness, 
as  accurately  as  you  can,  of  one  of  the  table-tops  in  the 
laboratory.  Get  the  dimensions  in  feet  and  fractions  of  a 
foot,  also  in  meters  and  fractions  of  a  meter.  Record  the 
measurements  in  your  note-book,  on  page  2.  After  con- 
sulting your  record,  answer  the  following  questions  : 

How  many  inches  are  there  in  each  of  the  three 
dimensions  ?•  How  many  centimeters  ?  How  many  milli- 
meters ? 

In  your  records  of  numerical  data  and  results,  use 
decimal  fractions  only. 

Experiment  1.      To  find  the  volume  of  a  solid  of  regular 


Apparatus.     A  meter  stick  ;  a  rectangular  block  of  wood. 

Directions.  (a)  Measure  and  record  the  length, 
breadth,  and  thickness  of  the  block  in  inches  and  fractions 
of  an  inch,  taking  four  measurements  of  the  length,  one 
along  each  of  the  four  edges  running  in  the  direction  of 
the  length,  four  of  the  breadth,  and  four  of  the  thickness. 
Find  the  average  length,  breadth,  and  thickness. 


EXPERIMENTAL    PHYSICS. 


In  making  the  measurements,  place  the  meter  stick  on 
its  narrow  side  (Fig.  1)  to  make  the  ends  of  the  gradu- 


m 

\     I     !     I     I     i     i 

0        1        2        3        4        5        C, 
1         1    1    1     1     1     II    1     1    1     1 

1     1    I    1    1     '     1    '    I     !jj 
7        8        19      60        1C 

l  1  1  1  l  1  1  1  18 

; 

FIG.  l. 

ations  come  close  to  the  block ;  do  not  use  the  divisions 
at  the  ends  of  the  stick,  as  the  ends  may  be  worn. 

Find  the  product  of  the  numbers  that  express  the 
average  length,  breadth,  and  thickness.  This  product 
will  be  the  number  of  cubic  inches  in  the  block. 

(b)  Using  the  same  care  as  in  (a),  find  the  dimensions  in 
centimeters  and  fractions  of  a  centimeter. 

From  the  average  length,  breadth,  and  thickness,  find 
the  number  of  cubic  centimeters  in  the  block. 

NOTE.     The  block  will  be  needed  for  the  next  two  experiments. 

Experiment  2.  To  find  the  weight  of  a  wooden  block  by 
means  of  a  spring  balance. 

Apparatus.  The  block  of  Exp.  1;  a  spring  balance  of  8-ounce 
capacity  (Fig.  2)  ;  thread. 

Directions.  Taking  care  that  the  balance  frame  touches 
nothing,  hang  it  by  its  ring  from  a  hook  or  other  suit- 
able support.  Place  your  head  in  such  a  position  that  the 
line  of  vision  passes  by  the  end  of  the  pointer  and  is  per- 
pendicular to  the  face  of  the  balance.  Observe  whether 
the  pointer  is  opposite  the  line  marked  0  (zero).  If  the 


MENSURATION. 


pointer  is  not  opposite  the  zero  line,  note  how  much 
above  or  below  it  is.  By  means  of  a  piece  of 
fine  thread  hang  the  block  on  the  hook  of  the 
balance,  and  observe  the  new  position  of  the 
pointer.  In  computing  the  result,  make  a  cor- 
rection for  the  "zero  error"  of  the  balance,  that 
is,  the  error  arising  if  the  pointer,  when  no 
weight  is  hung  on  the  hook,  is  not  exactly  in 
front  of  the  zero  line.  Strive  to  read  carefully 
to  the  tenths  of  the  smallest  divisions. 

Does  the  weight  of  the  thread  make  any 
difference  in  the  indications  of  the  balance  ? 

Making  use  of  the  result  obtained  in  Exp.  1 
(a),  what  do  you  find  to  be  the  weight  in  ounces 
of  one  cubic  inch  of  the  block  ? 


FIG.  2. 


Experiment  3.      To  find  the  weight  of  a  wooden  block 

by  means  of  a  platform 
balance. 

Apparatus.  The  block  of 
Exp.  1;  a  platform  balance; 
metric  weights. 

Directions.      Put  the 

rider  on  the  zero  notch 
of  the  balance  scale.  Wipe  the  pans  dry  and  clean.  Set 
the  pans  swinging,  and  add  bits  of  paper  till  they  swing 
evenly.  On  the  left-hand  pan  lay  the  block ;  on  the 
right-hand  pan  put  weights  (Fig.  3).  Use  the  rider  in 
making  the  final  adjustments.  Trust  the  indications  of 
a  swinging  balance  only.  (Why  ? )  Find  how  many 
grams  and  fractions  of  a  gram  the  block  weighs. 


6 


EXPERIMENTAL   PHYSICS. 


Making  use  of  the  results  obtained  in  Exp.  1  (5),  what 
do  you  find  to  be  the  weight  in  grams  of  one  cubic 
centimeter  of  the  block? 

Experiment  4.  To  find  the  volume  of  a  solid  of  irregu- 
lar shape. 

Apparatus.  A  100CC  graduate  (a  cylindrical  glass  vessel  marked 
off  into  cubic  centimeters) ;  a  piece  of  lead. 

Directions.  Fill  the  graduate  about  half  full  of  water 
and  note  the  exact  level  of  the  water.  Into  the 
water  put  the  piece  of  lead  (Fig.  4).  Be  sure 
that  it  is  entirely  beneath  the  surface.  (Why  ?) 
If  air-bubbles  cling  to  the  lead,  remove  by  shak- 
ing, but  take  care  not  to  spill  any  water.  Note 
the  level  at  which  the  water  now  stands.  As 
the  surface  of  the  water  is  highest  at  its  edge 
where  it  .meets  the  graduate,  get  the  level  by 
sighting  along  a  horizontal  line  that  just  grazes 
the  lowest  part  of  the  surface. 

How  many  cubic  centimeters  of  water  are 
displaced  ?  Is  the  volume  of  water  displaced  the 
same  as  the  volume  of  the  lead  ? 

How  many  cubic  centimeters  does  the  lead  contain  ? 

5.  Quantity ;  Unit ;  Numerical  Value.  In  the  ex- 
periments already  performed  we  have  made  measurements 
of  length,  volume,  and  weight,  and  in  our  subsequent 
work,  we  shall  often  make  measurements  of  other  magni- 
tudes, such  as  temperature,  friction,  and  electrical  resistance. 

Measured  magnitudes  are  called  quantities.  Every 
quantity  is  expressed  by  a  phrase  consisting  of  two  parts  : 
one  of  these  is  the  name  of  a  certain  known  quantity 


FIG.  4. 


DENSITY.  « 

which  is  taken  as  a  standard  of  reference,  and  which  is  of 
the  same  kind  as  the  quantity  to  be  expressed ;  and  the 
other  is  a  number  which  shows  how  many  times  the 
standard  is  to  be  taken  in  order  to  make  up  the  required 
quantity.  The  standard  quantity  is  called  the  unit,  and 
the  number  the  numerical  value  of  the  quantity. 

There  are  as  many  units  as  there  are  different  kinds  of 
quantities  to  be  measured. 

In  this  book  the  cubic  inch  is  taken  as  the  unit  of 
volume  and  the  ounce  as  the  unit  of  weight  for  the 
English  System,  except  for  the  measurement  of  large 
quantities,  when  the  cubic  foot  and  the  pound  are  used ; 
for  the  Metric  System  the  cubic  centimeter  is  taken  as 
the  unit  of  volume  and  the  gram  as  the  unit  of  weight. 

The  distance  from  one  end  of  the  Capitol  at  Washing- 
ton to  the  other  is  just  751  feet.  The  phrase  "  751  feet " 
tells  the  number  of  units  of  a  particular  kind  contained  in 
the  distance  mentioned.  In  this  case  the  foot  is  the  unit, 
while  751  is  the  numerical  value  of  the  quantity. 

QUESTIONS.  What  is  the  unit  and  what  is  the  numerical  value  in 
each  of  the  following  expressions  of  quantity  :  72  feet  ?  10  meters  ? 
202  cubic  centimeters  ?  8  grains  ?  7  ounces  ?  100  cubic  feet  ?  10  inches  ? 

DENSITY. 

6.  Density.  The  final  result  of  Exp.  2  gave  the 
weight  in  ounces  of  one  cubic  inch  of  the  block,  while 
that  of  Exp.  3  gave  the  weight  in  grams  of  one  cubic 
centimeter  of  the  block. 

Definition.  By  the  density  of  a  substance  is  meant  the 
weight  of  one  unit  of  volume  of  the  substance. 


8  EXPERIMENTAL    PHYSICS. 

NOTE.  Later  in  the  course  we  shall  limit  the  meaning  of  the  word 
weight  in  this  definition  to  that  expressed  by  the  word  mass,  and  we  shall 
show  that  a  platform  balance  and  not  a  spring  balance  should  be  used  in 
our  method  of  getting  the  density  in  the  English  System. 

The  final  result  of  Exp.  2,  then,  gave  the  density  of 
the  block  in  the  English  System  ;  the  final  result  of 
Exp.  3,  the  density  in  the  Metric  System. 

The  student  should  consult  Exps.  1,  2,  and  3,  and  on 
the  right-hand  page  of  his  note-book,  the  one  opposite  the 
last  left-hand  page  that  has  been  written  on,  give  a  brief 
account  of  the  method  of  finding  the  density  of  a  rect- 
angular block  of  wood,  which  shall  apply  to  either  the 
English  System  or  the  Metric. 

When  the  Metric.  System  was  planned,  it  was  decided 
to  take  the  density  of  water  as  unity,  that  is,  to  take  the 
weight  of  a  cubic  centimeter  of  water  as  the  unit  of 
weight,  and  to  call  it  the  gram,  hence 

A  cubic  centimeter  of  water  weighs  a  gram. 

NOTE.  Strictly  speaking,  however,  in  order  that  a  cubic  centimeter 
of  water  may  weigh  a  gram,  the  water  must  be  pure  and  it  must  have  a 
certain  temperature  a  few  degrees  above  freezing  ;  but  for  our  purposes 
common  water  at  any  ordinary  temperature  will  give  results  sufficiently 
accurate. 

7.  Precautions  to  be  taken  in  Measurements  and 
Computations.  With  a  meter  stick,  such  as  you  have 
used,  suppose  a  rectangular  block  to  have  been  measured 
in  centimeters  with  the  following  results  : 

MEASUREMENTS  MEASUREMENTS  MEASUREMENTS 

OF  LENGTH.  OF  BREADTH.  <u   THICKNESS. 

cm.  cm.  cm.     . 

7.30  6.40  3.12 

7.32  6.40  3.10 

7.32  6.41  3.11 

7.33  6.42  3.14 


MEASUREMENTS  AND  COMPUTATIONS. 

It  will  be  noticed  that  7.30cm  in  the  record  just  given 
does  not  mean  exactly  the  same  thing  as  7.3cm.  The 
former  shows  that  the  hundredths  of  a  centimeter  could  be 
estimated,  and  that  you  have  found  that  the  length  is 
more  nearly  7.30cm  than  7.29cm  or  7.31cm.  The  latter 
means  that  the  hundredths  of  a  centimeter  were  not  taken 
into  account.  Consequently,  unless  you  are  careful  to 
estimate  the  hundredths  of  centimeters,  you  must  write 
not  7.30cm,  but  7.3cm. 

If  we  add  each  of  the  columns,  and  divide  each  sum  by 
4  to  get  the  average  length,  breadth,  and  thickness,  we 
have  : 

4)25.63 
6.41 

Since  the  millimeter  was  the  smallest  division  on  the 
meter  stick,  and  since  we  had  to  estimate  the  tenths  of  a 
millimeter,  the  second  decimal  place  in  each  of  the 
measurements  is  in  doubt ;  hence  the  second  decimal 
place  in  each  of  the  averages  is  in  doubt.  Consequently, 
in  each  average,  we  have  discarded  as  wholly  doubtful  all 
figures  after  the  second  place  of  decimals.  It  will  be 
seen,  however,  by  examining  the  averages,  that  the  last 
figure  retained  has  been  increased  by  unity  (one)  when- 
ever the  first  figure  discarded  is  5  or  greater  than  5.  It 
is  not  only  a  waste  of  time  to  obtain  and  to  record  the 
average  beyond  the  first  doubtful  figure,  but  is  also  inac- 
curate, since  it  is  understood  in  physics  that  the  observer 
claims  as  accurate  all  the  figures  in  the  record  of  a 
measurement  except  the  last. 


10  EXPERIMENTAL   PHYSICS. 

We  have,  then : 

Average  length  =  7.32cm. 
Average  breadth  =.  6.41cm. 
Average  thickness  =  3.12cm. 

For   the   sake    of   clearness   the   doubtful   figures  are 
printed  in  full-faced  type. 

Let  us  compute  the  volume  of  the  block. 

Volume  of  the  block  =  7.32  X  6.41  X  3.12. 

7.32  46.9 

6.41  3.12 

732  938 

2928  469 

4392  14O7 


46.9212  146.328 

The  final  result  is  to  be  entered  as  146CC. 

In  the  future  it  will  be  understood  that  the  last  figure 
recorded  in  the  value  of  a  measurement  is  in  doubt. 

Let  the  student  turn  back  to  his  record  of  experiments 
performed,  and,  allowing  the  old  computations  to  stand, 
reckon  the  results  once  more  in  accordance  with  the 
following  rules  : 

1.  In  all  averages  keep  but  one  doubtful  figure.     (If  the 
figure  following  the  doubtful  one  is  5  or  greater  than  5, 
increase  the  doubtful  figure  by  unity.) 

2.  After  multiplying  two  numbers  together,  keep  in  the 
result  as  many  figures  of  the  product,  counting  from  the 
left,  as  there  are  figures  in  the  smaller  factor. 


SPECIFIC   GRAVITY.  11 

3.  After  dividing  one  number  by  another,  keep  in  the 
quotient,  counting  from  the  left,  as  many  figures  as  there  are 
in  the  smaller  of  the  two. 

In  subsequent  experiments,  these  rules  must  always 
govern  your  measurements  and  computations. 


SPECIFIC    GRAVITY. 

8.  Specific  Gravity.  The  object  of  the  following 
experiment  is  to  make  clear  to  the  student  the  meaning 
of  the  term  specific  gravity. 

Experiment  5.  To  find  how  many  times  as  heavy  as 
an  equal  volume  of  water  a  piece  of  lead  is. 

Apparatus.  A  100CC  graduate ;  a  piece  of  lead  that  weighs 
more  than  1008  (grams)  ;  a  platform  balance. 

Directions.  Find  the  weight  in  grams  of  a  piece  of 
dry  lead.  Find  the  volume  of  the  lead  in  cubic  centi- 
meters (by  method  of  Exp.  4). 

With  the  data  obtained,  and  knowing  that  a. cubic  centi- 
meter of  water  weighs  a  gram,  find  how  many  times  as 
heavy  as  an  equal  volume  of  water  the  lead  is. 

The  number  thus  obtained  is  called  the  specific  gravity 
of  lead. 

Definition.  The  number  obtained  by  dividing  the  weight 
of  a  substance  by  the  weight  of  an  equal  volume  of  water  is 
called  the  specific  gravity  of  the  substance. 

NOTE.  For  all  work  in  this  course  use  common  water  at  any  ordinary 
temperature. 


12 


EXPERIMENTAL   PHYSICS. 


9.  Principle  of  Archimedes.  The  next  two  experi- 
ments have  for  their  object  the  unfolding  of  the  celebrated 
Principle  of  Archimedes.1  The  use  of  this  principle  will 

enable  us  to  determine 
with  ease  the  specific 
gravity  of  substances. 

Experiment    6.       To 

find  the  relation  between 
the  weight  of  a  body  that 
will  float  in  water  and 
the  weight  of  water  it 
displaces. 

Apparatus.  A  100CC 
graduate  ;  a  200 cc  beaker ;  a 
copper  vessel  with  a  spout 
to  which  a  rubber  tube  10cm 
long  is  attached;  a  wooden 

block  whose  corners  are  rounded,  if  necessary,  to  allow  it  to  be  put 

into  the  vessel ;  a  platform  balance. 

Directions.  Find  the  weight  of  the  block  in  grams. 
Fill  the  vessel  with  water  till  some  runs  off  through  the 
tube  attached  to  the  spout.  This  tube  should  not  be 

1  Archimedes  (287-212  B.C.),  a  famous  mathematician  of  Syracuse  in 
Sicily,  was  asked,  so  the  story  runs,  by  Hiero,  king  of  Syracuse,  to  find 
whether  a  certain  crown  of  the  king's  was  of  pure  gold  or  of  gold  alloyed 
with  silver.  Archimedes  asked  for  time  to  reflect  on  the  problem.  Soon 
afterwards,  when  in  his  bath,  he  noticed,  what  he  had  probably  never 
carefully  observed  before,  that  his  body  was  pressed  upwards  with  a  force 
which  increased  the  more  completely  he  was  immersed  in  the  water ;  to 
his  subtle  intellect  this  discovery  suggested  a  way  of  solving  the  king's 
problem.  By  careful  experiments  he  discovered  that  of  equal  masses  of 
gold  and  silver  the  silver  weighed  less  in  water  than  the  gold.  On 
making  the  test,  he  found  the  crown  to  weigh  less  in  water  than  an  equal 
mass  of  gold,  so  he  concluded  that  the  crown  was  not  of  pure  gold. 


FIG.  5. 


SPECIFIC    GRAVITY. 


13 


touched  during  the  experiment.  When  water  stops  flow- 
ing, carefully  put  the  block  flatwise  into  the  water 
(Fig.  5),  and  in  the  beaker  catch  all  the  water  that  flows 
out.  Measure  this  water  in  the  graduate. 

How  many  cubic  centimeters  of  water  does  the  block 
displace  ? 

How  much  does  a  cubic  centimeter  of  water  weigh? 

How  many  grams  of  water  does  the  block  displace  ? " 

Is  the  weight  of  water  displaced  the  same,  or  nearly  the 
same,  as  the  weight  of  the  block  ? 

Can  you  infer  any  relation  between  the  weight  of  a 
body  that  will  float  and  the  weight  of  water  it  displaces  ? 

QUESTION.  If  a  wooden 
block  weighs  100s,  how  many 
grams  of  water  will  it  dis- 
place when  floating  in  water? 

Experiment  7.  To 
find  how  much  less  a 
body  that  will  sink 
weighs  in  water  than 
in  air. 


Apparatus.  A  spring 
balance  of  30-pound  ca- 
pacity ;  a  heavy  iron  ball 
with  a  handle  to  which  a 
string  is  attached  (an  iron 
safety-valve  weight,  weigh- 
ing at  least  12  pounds)  ;  a 
dipper ;  a  pail.  FIG.  6. 

Directions.  Perform  the  experiment  at  the  sink. 
By  its  ring  hang  the  balance  to  a  stout  support,  and  find 
the  Aveight  of  the  ball. 


14  EXPERIMENTAL   PHYSICS. 

Then,  taking  care  that  the  ball  does  not  touch  the  pail, 
let  it  hang  by  the  string,  as  in  Fig.  6,  from  the  hook  of 
the  balance  so  that  it  will  be  completely  covered  by  the 
water  in  the  pail  in  the  sink.  As  it  hangs  immersed  in 
the  water,  find  its  weight. 

Remove  the  ball  from  the  balance  and  hang  the  pail  in 
its  place.  With  the  dipper  fill  the  pail  brimful  of  water, 
and  get  the  weight.  Now  lower  the  ball  into  the  pail 
until  it  is  completely  beneath  the  surface,  holding  it  by 
the  string  till  the  water  stops  flowing  over  the  edge  of 
the  pail;  then  carefully  remove  the  ball,  and  note  the 
weight  of  the  pail  and  the  water  left. 

How  much  less  did  the  ball  weigh  in  water  than  in  air  ? 

Did  the  ball  displace  its  own  volume  of  water? 

What  is  the  weight  of  the  water  displaced  by  the  ball? 

Can  you  infer  any  relation  between  the  weight  of  water 
displaced  and  the  apparent  loss  in  weight  of  the  ball  ? 

The  inferences  from  the  results  of  Exps.  6  and  7  are 
together  known  as  the  Principle  of  Archimedes.  Try  to 
frame  a  concise  statement  that  shall  include  both  of  your 
inferences. 

QUESTION.  If  a  cubic  centimeter  of  iron  weighs  7&,  what  will  be 
its  apparent  weight  if  plunged  under  water  ? 

1C.    Applications   of  the   Principle   of  Archimedes. 

With  one  exception,  the  next  six  experiments  involve  the 
use  of  the  Principle  of  Archimedes. 

Experiment  8.  To  find,  without  the  use  of  a  balance, 
the  specific  gravity  of  a  piece  of  wood. 

Apparatus.  The  same  as  that  used  in  Exp.  6,  without  the 
balance. 


SPECIFIC    GRAVITY. 


15 


Directions.  By  the  method  of  displacement  of  water 
(see  Exp.  6)  find  the  weight  of  the  wood.  Then  press 
the  wood  down  into  the  water  until  completely  covered. 
Catch  the  water  and  measure  it. 

What  do  you  find  the  volume  of  the  wood  to  be  in. 
cubic  centimeters  ?  What,  then,  is  the  weight  of  a  volume 
of  water  of  the  same  size  as  the  wood?  What  is  the 
specific  gravity  of  the  wood  ?  In  what  way  has  the  Prin- 
ciple of  Archimedes  helped  you  in  this  experiment? 

QUESTION.     If  the  specific  gravity  of  white  wood  is  0.5,  how  deep 
will  a  rectangular  block  of  white 
wood  sink  in  water  ? 

Experiment  9.      To 

find,  by  submersion  with 
a  sinker,  the  specific  grav- 
ity of  a  piece  of  wood. 

Apparatus.  A  rectangular 
block  of  wood  ;  a  platform 
balance  standing  on  a  wooden 
support ;  a  piece  of  lead  heavy 
enough  to  sink  the  block;  a 
glass  jar  three-quarters  full  of 
water ;  a  piece  of  thread. 

Directions.  Weigh 
the  block  to  O.lg.  Over 
the  left-hand  pan  of  the 
balance,  as  shown  in  Fig. 
7,  loop  the  thread  so  that  it  will  touch  nothing  but  the  pan 
and  the  water.  Fasten  the  lead  to  the  thread,  and  find  how 
much  the  lead  weighs  when  completely  submerged  in  water 
without  touching  either  the  sides  or  the  bottom  of  the 
jar.  If  air-bubbles  are  on  the  lead,  brush  them  off. 


FIG.  7. 


16  .EXPERIMENTAL   PHYSICS. 

Fasten  the  lead  to  the  block,  and,  when  entirely  under 
water  and  touching  neither  the  bottom  nor  the  sides  of 
the  jar,  weigh  both  to  O.lg. 

If  the  block  were  unattached  to  the  sinker,  and  floating, 
by  how  many  grams  would  the  water  buoy  it  up  ?  (See 
your  inference  from  Exp.  6.) 

When  the  sinker  is  fastened  to  the  wood,  and  both  are 
completely  submerged,  by  how  many  grams  more  does 
the  water  buoy  up  the  block  than  it  did  before  ;  that  is, 
what  is  the  difference  between  the  weight  of  the  sinker 
alone  in  water  and  the  joint  weight  of  sinker  and  block 
in  water  ?  What  is  the  weight  of  a  volume  of  water  of 
the  same  size  as  that  of  the  block  ?  (In  answering  this 
question,  consider  carefully  your  answers  to  the  two 
preceding  ones.) 

What  is  the  specific  gravity  of  the  block  ? 

NOTE.     After  drying  the  block,  use  it  in  the  next  experiment. 

Experiment  1O.  To  find,  by  flotation,  the  specific  gravity 
of  a  piece  of  wood. 

Apparatus.  The  block  used  in  Exp.  9  ;  a  meter  stick ;  a  glass 
jar  nearly  full  of  water. 

Directions.  By  taking  measurements  at  each  corner, 
get  the  average  thickness  of  the  block.  Taking  care  that 
no  air-bubbles  cling  to  the  under  surface  or  to  the  sides  of 
the  block,  gently  lay  it  on  the  surface  of  water  in  the  jar. 
If  the  sides  of  the  block  are  not  oiled,  the  water  will 
creep  up  a  little  way,  but  if  the  block  has  been  oiled,  the 
water  close  to  the  block  will  be  slightly  depressed.  [This 
phenomenon,  either  the  creeping  up  of  the  water,  or  its 


SPECIFIC   GRAVITY.  17 

depression,  belongs  to  a  class  included  under  the  name 
capillary  action  (from  the  Latin  capillus,  hair),  as  the 
phenomenon  was  first  observed  in  tubes  of  fine,  hair-like 
bore.]  With  the  eye  on  a  level  with  the  water,  sight, 
through  the  sides  of  the  jar,  at  the  block,  and  see  where 
the  general  level  of  the  water  would  meet  the  block. 
Remove  the  block  carefully.  With  a  fine  pointed  lead- 
pencil,  and  guided  by  the  water-line,  make  a  dot  at  each 
corner  where  the  water  would  have  met  the  block  had 
it  not  been  for  capillary  action.  Now  measure  from  each 
of  the  dots  to  the  lower  surface  of  the  block,  and  find  the 
average  depth  to  which  the  block  sank. 

The  following  is  the  course  of  reasoning  by  which  the 
specific  gravity  may  be  found : 

Imagine  a  block  of  water  of  the  same  size  as  the  part  of 
the  wooden  block  under  water. 

What  relation  exists  between  the  weight  of  this  volume 
of  water  and  the  weight  of  the  wooden  block  ?  (See  your 
inference  from  Exp.  6.) 

Imagine  another  block  of  water  of  the  same  size  as  the 
wooden  block. 

These  two  blocks  of  water,  which  you  have  imagined, 
have  equal  bases  but  unequal  heights. 

Is  the  weight  of  the  thinner  block  the  same  part  of  the 
weight  of  the  thicker  that  the  height  of  the  thinner  block 
is  of  the  height  of  the  thicker  ? 

What  is  the  specific  gravity  of  the  wood  ? 

In  getting  the  specific  gravity  in  this  case,  "have  you 
made  direct  use  of  the  weight  of  the  block  and  the  weight 
of  an  equal  volume  of  water? 


18  EXPERIMENTAL    PHYSICS. 

Experiment  11.  To  find,  by  the  specific  gravity  bottle, 
the  specific  gravity  of  a  liquid. 

.  Apparatus.  A  small  bottle  having  a  wide  mouth  (this  is  called 
the  "specific  gravity  bottle"),  with  a  glass  stopple,  and  of  2-ounce  or 
3-ounce  capacity  ;  a  platform  balance  ;  a  piece  of  cloth  or  a  towel 
with  which  to  dry  the  bottle  ;  water  ;  kerosene. 

Directions.  Wipe  the  bottle  dry  both  inside  and  out. 
Weigh  the  bottle  together  with  the  stopple,  which  should 
fit  tightly.  Weigh  the  bottle  full  of  kerosene.  When 
putting  in  the  stopple,  take  care  to  exclude  air-bubbles. 
The  best  way  to  do  this  is  to  fill  the  bottle  brimful,  then 
push  the  stopple  into  place.  Weigh  the  bottle  full  of  water. 

What  weight  of  kerosene  did  the  bottle  hold  ? 

What  weight  of  water  did  the  bottle  hold  ? 

Was  the  volume  of  kerosene  equal  to  that  of  the  water  ? 

What  is  the  specific  gravity  of  kerosene  ? 

In  getting  the  specific  gravity  in  this  case,  have  you 
made  direct  use  of  the  weight  of  the  kerosene  and  the 
weight  of  an  equal  volume  of  water? 

Have  you  made  use  of  the  Principle  of  Archimedes  ? 

Experiment  12.  To  find,  by  means  of  buoyant  action, 
the  specific  gravity  of  a  liquid. 

Apparatus.  A  jar  three-quarters  full  of  kerosene  ;  a  jar  three- 
quarters  full  of  water  ;  a  platform  balance  with  support ;  a  piece  of 
lead  or  iron  weighing  100s  or  more  ;  a  piece  of  thread. 

Directions.  Weigh  the  piece  of  lead.  With  the 
thread  suspend  the  lead  from  the  balance  pan,  and  weigh 
in  kerosene.  Take  the  lead  from  the  kerosene,  wipe  dry, 
and  find  its  weight  in  water. 


srtfiv: 


SPECIFIC    GRAVITY. 

What  weight  of  water  did  the  lead  displace  ?  (See 
your  inference  from  Exp.  7.)  What  weight  of  kerosene 
did  the  lead  displace  ?  Was  the  volume  of  kerosene  dis- 
placed by  the  lead  the  same  as  the  volume  of  water  ? 

What  is  the  specific  gravity  of  kerosene  ? 

Have  you  made  use  of  the  Principle  of  Archimedes  ? 

Now  that  you  have  performed  the  experiment,  what, 
should  you  say,  is  the  meaning  of  the  term  "buoyant1 
action  "  ? 

Experiment  13.  To  find  the  specific  gravity  of  a  solid 
that  will  sink  in  water. 

Apparatua  A  glass  bottle  without  stopple  (the  glass  bottle  used 
in  Exp.  11  will  answer);  a  platform  balance  on  a  support ;  a  piece 
of  thread  ;  a  jar  of  water. 

Directions.  Weigh  the  bottle  empty.  Also  weigh  the 
bottle  in  water,  after  filling  it  with  water.  See  that  every 
part  of  the  bottle  is  beneath  the  surface  of  the  water, 
and  that  there  are  no  air-bubbles  in  the  bottle. 

What  is  the  weight  of  a  volume  of  water  of  the  same 
size  as  the  volume  of  the  glass  ? 

What  is  the  specific  gravity  of  the  glass  ? 

Had  the  glass  forming  the  bottle  been  in  a  solid  lump, 
would  the  result  have  been  different  ? 

Have  you  made  use  of  the  Principle  of  Archimedes  ? 

11.  Agreement  between  Specific  Gravity  and  Den- 
sity in  the  Metric  System.  If  the  student  compares 
the  result  of  either  Exps.  8  or  9  with  that  of  Exp.  2  and 
that  of  Exp.  3,  the  specific  gravity  of  wood  with  its 

1  When  a  word  or  a  term  occurs  the  meaning  of  which  is  not  perfectly 
clear,  consult  a  good  dictionary. 


20  EXPERIMENTAL   PHYSICS. 

density  in  the  English  System  and  in  the  Metric,  he 
cannot  fail  to  notice  that  the  specific  gravity  is  widely 
different  from  the  numerical  value  of  the  density  in  the 
English  System,  while  it  agrees  closely  with  the  numer- 
ical value  of  the  density  in  the  Metric.  This  agreement 
does  not  come  by  chance,  but  is  the  result  of  the  relation 
which,  in  the  Metric  System  of  weights  and  measures, 
exists  between  the  unit  of  volume  and  the  unit  of  weight. 
For  example,  to  get  the  specific  gravity  of  a  piece  of 
wood,  we  divide  its  weight  by  the  weight  of  an  equal 
volume  of  water ;  on  the  other  hand,  to  get  the  density  of 
the  piece  of  wood,  we  divide  its  weight  by  the  numerical 
value  of  its  volume.  In  the  Metric  System  one  cubic 
centimeter  of  water  weighs  one  gram  ;  so  the  numerical 
value  of  the  volume  of  a  body  is  equal  to  the  numerical 
value  of  the  weight  of  a  like  volume  of  water ;  hence, 
the  quotients  resulting  from  the  divisions  must  be  equal 
in  numerical  value. 

EXAMPLES. 

1.  A  piece  of  wood  weighs  75&,  and  its  density  is  0.5s  per  cubic  cen- 
timeter.    What  is  its  volume  ? 

2.  A  body  weighs  100s  in  air,  and  75e  in  water.     What  is  the  specific 
gravity  of  the  body  ? 

3.  A  body  lighter  than  water  weighs  lOOg  hi  air.     A  sinker,  weighing 
50s  in  water,  is  attached  to  the  body,  and  their  combined  weight  in  water 
is  25s.     What  is  the  specific  gravity  of  the  body  ? 

4.  What  is  the  specific  gravity  of  water  ? 

5.  A  cubic  decimeter  (a  cube  whose  edges  are  10cm)  of  wood  sinks  to 
a  depth  of  6cm  in  water.     Find  the  specific  gravity  of  the  wood. 

6.  A  specific  gravity  bottle  weighs,  when  empty,  1000& ;  when  filled 
with  kerosene,  1800s ;  when  filled  with  water,  2000s.     Find  the  specific 
gravity  of  kerosene. 

7.  Weight  of  a  sinker  in  air,  50s  ;  in  kerosene,  42.  Is  j  in  water,  40s. 
Find  the  specific  gravity  of  kerosene. 


PNEUMATICS. 


21 


8.  A  piece  of  wood  of  irregular  shape  floats  with  -  of  its  volume 
under  water.     What  is  its  specific  gravity  ? 

Solution.      If  we  let  1  represent  the  weight  of  a  volume  of  water 
equal  to  that  of  the  wood,  the  weight  of  the  wood  will  (by  Principle 

b 
of  Archimedes,  Exp.  6)  be  -  x  1,  or  -•     Hence  sp.  gr.  =  y  =  -• 

9.  An  iceberg  floats  with  one-ninth  of  its  volume  above  the  water. 
Find  the  specific  gravity  of  the  iceberg. 

10.  Let  us  suppose    that    Hiero's    crown  (see  Art.   9)  weighed  10 
ounces,  and  that  its  specific  gravity  was  15.     If  the  specific  gravity  of 
gold  is  19.3,  and  the  specific  gravity  of  silver  is  10.5,  find  the  weight  of 
silver  in  the  crown. 

Solution.     Let  x  denote  the  weight  of  silver  in  the  crown. 
Then  10 -x  will       "        "        "        "gold    "    " 

Weight  of  water  whose  volume  equals  that  of  silver  =  — — -  • 

10  —  x 

1 1          u        u  u  u  u  titt    gold.     —  —     • 

19.3 
By  the  definition  of  specific  gravity,  we  have  —  —  =  15. 

X       i     1U  ~~  «C 

10.6       10.3 

Clearing  of  fractions,  taking  out  common  factors,  and  combining,  we 
find  8.8 x  =  30.1,  whence  x  =  3.42  ounces. 

11.  A  diamond  ring  weighs  65  grains  in  air,  and  60  in  water.     Find 
the  weight  of  the  diamond,  the  specific  gravity  of  gold  being  17.5,  and 
that  of  the  diamond  3.5. 


PNEUMATICS. 

12.  Air.  The  earth  on  which  we  live  is  surrounded  by 
a  gas  which  we  call  air.  Although  we  cannot  see  it,  its 
existence  is  proved  to  us  by  our  being  able  to  feel  it. 
When  we  are  riding  fast  we  feel  the  air.  The  whole 
mass  of  this  air  is  called  the  atmosphere, 


22  EXPERIMENTAL   PHYSICS. 

We  shall  now  study  in  the  next  three  experiments 
some  of  the  properties  of  air  which  come  under  the  head 
of  Pneumatics. 

Experiment  14.      To  find  whether  air  has  weight. 

Apparatus.  An  air-pump;  a  piece  of  "pressure"  tube  with  a 
pointed  glass  tube  in  one  end  attached  to  the  exhaust  nozzle ;  a 
2-quart  glass  bottle  with  a  perforated  rubber  stopple,  having  a  glass 
tube  thrust  through  with  a  piece  of  pressure  tube  10cm  long 
attached ;  a  small  brass  clamp  ;  a  platform  balance  ;  vaseline. 

Directions.  Into  the  mouth  of  the  bottle  insert  the 
stopple  slightly  smeared  with  vaseline  to  make  the  bottle 
air-tight.  Over  the  tubing  slip  the  clamp  so  that  it  fits 
loosely. 

Weigh  the  bottle  together  with  stopple,  tubes,  and 
clamp.  The  result  is  the  weight  of  the  bottle  filled  with 
air.  Lay  the  bottle  on  the  table  close  to  the  air-pump. 
Push  the  end  of  the  rubber  tube  over  the  pointed  glass 
tube  attached  to  the  pump.  Without  hurrying,  make  20 
strokes  of  the  pump  (a  stroke  is  one  complete  up-and- 
down  movement  of  the  handle).  Some  of  the  air  has  now 
been  pumped  out.  Screw  the  clamp  tightly  on  the  rubber 
tube  attached  to  the  .bottle.  Remove  the  bottle  and  weigh. 

If  there  is  a  difference  between  the  two  weights,  how 
do  you  account  for  it  ? 

Experiment  15.  To  find  whether  the  atmosphere  presses 
equally  in  all  directions. 

Apparatus.  An  air-pump ;  a  thick-walled  "  thistle-tube  "  whose 
mouth,  about  2.5cm  in  diameter,  has  a ,  piece  of  thin  sheet  rubber, 
like  that  which  dentists  use,  stretched  across,  and  firmly  fastened  by 
a  piece  of  strong  thread  wound  round  the  tube  just  back  of  the  lip, 
as  shown  in  Fig.  8  (the  piece  of  sheet  rubber  thus  arranged  is  called 
a  diaphragm) ;  a  piece  of  pressure  tube  30cm  long. 


PNEUMATICS.  23 

Directions.  By  means  of  the  pressure  tube  connect 
the  stem  of  the  thistle-tube  with  the  air-pump.  Make 
one  or  two  strokes  of  the  air-pump.  Take  care  not  to  burst 
the  diaphragm.  The  diaphragm  will  be  forced  into  a  deep 
cup-shape  by  the  pressure  of  the  atmosphere.  To  prevent 
air  from  leaking  into  the  thistle-tube  from  the  pump, 
pinch  the  tube  tightly.  Watching  the  curvature  of  the 
diaphragm,  turn  the  mouth  of  the  tube  up,  down,  and  in 
many  directions. 

As  you  turn  the  mouth  of  the  tube  in  different  direc- 
tions, does   the  shape 
of     the    diaphragm 
change  ? 

What  inference  can 
you  draw  ? 

Pneumatics  is  that 
branch  of  physics  which 
treats  of  the  mechani- 
cal properties  of  air,  as  weight  and  pressure. 

Experiment  16.  To  find  whether  the  pressure  of  the 
atmosphere  upon  a  given  surface  depends  on  the  shape  of 
the  passage  by  which  it  reaches  the  surface. 

Apparatus.  A  small  thistle-tube  with  a  rubber  diaphragm  across 
the  mouth,  about  1.5cm  in  diameter,  and  a  piece  of  rubber  tube 
5Qcin  long  attached  to  the  stem. 

Directions.  With  one  side  of  the  diaphragm  the  air 
communicates  directly,  but  with  the  other  indirectly 
through  the  tube.  If,  without  compressing  the  tube, 
you  bend  it  into  different  shapes,  you  will  be  able,  by 


24  EXPERIMENTAL    PHYSICS. 

watching  the  diaphragm,  to  decide  whether  there  is  any 
change  of  pressure  on  the  "given  surface,"  the  side  of 
the  diaphragm  in  the  thistle-tube. 

What  inference  can  you  draw  from  this  experiment  ? 


LIQUID    PRESSURE. 

13.  Liquid  Pressure.  We  shall  now  study  the  laws 
which  govern  pressure  in  liquids. 

Experiment  17.  To  find  whether  the  pressure  increases 
with  the  depth  below  the  surface. 

Apparatus.  A  pail  three-quarters  full  of  water;  a  pressure- 
gauge. 

Directions  for  Making  the  Pressure-Gauge.  Beneath 
the  surface  of  water  in  the  pail  dip  one  end  of  a  piece  of 
thermometer  tube  whose  length  is  about  15cm.  When 


FIG.  9. 

the  end  is  about  lcm  below  the  surface,  cover  it  with  the 
finger  and  remove  the  tube.  The  little  thread  of  water 
about  lcm  long  thus  caught  in  the  tube  is  called  an  index. 
Turn  the  tube  into  a  horizontal  position,  and  remove  the 
finger  from  the  end.  By  gentle  shaking,  get  the  index 
placed  at  about  one-fourth  the  length  of  the  tube  from 
one  end;  over  this  end,  which  should  have  been  heated 


LIQUID    PKESSUKE.  25 

and  drawn  out,  carefully  slip  the  rubber  tube  attached  to 
the  thistle-tube  of  Exp.  16,  and  push  it  on  till  it  covers 
about  lcm  of  the  glass  tube.  Take  care  not  to  kink,  or 
bend  sharply,  or  compress  the  rubber  tube,  lest  you  force 
the  index  out.  Make  a  rubber  ring  by  cutting  a  thin  slice 
from  a  rubber  tube.  Push  the  glass  tube  into  this  ring. 
The  gauge  is  now  completed,  as  shown  in  Fig.  9.  In  using 

it,  be  sure  the  tube  contain- 
ing the  index  is  horizontal. 
A  convenient  form  of  the  gauge  is 
shown  in  Fig.  10,  where  the  thistle- 
tube    and   the    tube    containing   the 
index  are  held  in  position  by  a  metal- 
lic frame.     By  means  of   the  little 
crank   and   a   rubber  belt,   a  rotary 
motion  can  be  given  to  the  thistle- 
tube. 

What  happens  to  the  index  when 
you  press  lightly  against  the  dia- 
phragm? If  you  hold  the  thistle- 
tube  clasped  in  the  palm  of  your 
hand,  does  the  index  move? 

(We  shall  study  this  question  more  care- 
fully in  the  chapter  on  Heat.) 

Directions.  Beside  the  pail  upon  the  table  lay  the 
glass  tube  of  the  gauge;  along  this  tube  push  the  little 
rubber  ring  (the  "marker")  till  it  is  over  one  end  of  the 
index.  With  one  hand  steady  the  glass  tube,  with  the 
other,  using  great  care  not  to  kink,  or  bend  sharply,  or 
compress  the  rubber  tube,  lower  the  thistle-tube  into  the 
pail  (Fig.  11),  which  should  contain  water  that  has  stood 


26 


EXPERIMENTAL   PHYSICS. 


FIG.  11. 


in  the  room  for  several  hours,  to  ensure  that  its  tempera- 
ture shall  be  nearly  the  same  as  that  of  the  room.  As  the 
thistle-tube  goes  deeper  and  deeper  below  the  surface, 
watch  the  index. 

How  does  the  index  act?     What  inference   can   you 

draw  from  this  action? 
With  what  are  the 
thistle -tube  and  the 
rubber  tube  filled? 
By  what  means  is  the 
pressure  sent  from 
the  diaphragm  to  the 
index  ? 

Experiment  18. 

To  find  whether  the 
pressure  at  a  given  point  in  a  liquid  is  the  same  in  all 
directions. 

Apparatus.     The  same  as  in  Exp.  17. 

Directions.  On  the  inside  of  the  pail,  a  little  way 
below  the  surface  of  the  water,  make  a  dot.  Keeping  its 
center  on  a  level  with  this  dot  and  at  a  given  distance 
from  the  dot,  turn  the  diaphragm  so  that  it  will  face  in 
various  directions,  downwards,  horizontally,  and  obliquely. 

What  do  you  infer  from  the  action  of  the  index  ? 

Compare  your  inference  with  that  of  Exp.  15. 

When,  as  in  this  experiment,  the  tube  of  the  gauge  is 
bent  into  different  curves,  what  reason  have  you  for 
thinking  that  the  pressure  transmitted  by  the  air  in  the 
tube  does  not  change  in  passing  round  the  curves  ?  (See 
your  inference  from  Exp.  16.) 


LIQUID   PRESSURE. 


27 


Experiment  19.  To  find  whether  the  pressure  at  all 
points,  in  a  horizontal  plane  passing  through  the  liquid,  is 
equally  great. 

Apparatus.  The  pressure-gauge ;  two  student-lamp  chimneys  ;  a 
retort-stand  with  two  clamps  each  large  enough  to  hold  a  chimney ; 
two  good  cork  stopples  to  fit  the  smaller  end  of  each  chimney  ;  a  pail 
of  water ;  some  cement  made  by  melting  together  equal  parts  of 
beeswax  and  rosin. 

PART  1.  Where  it  is  possible  to  pass  along  a  straight 
line  from  one  point  to  any  other  in  the  plane. 

Directions.  Dip  the  stopples  into  the  melted  cement 
and  stop  the  smaller  end  of  each  chimney  air-tight.  Fill 


FIG.  12. 

one  of  the  chimneys  with  water.  Placing  the  hand  or  a 
piece  of  wet  paper  over  the  open  end,  invert  and  lower 
the  chimney  into  the  pail  of  water.  When  the  covered 
end  is  below  the  surface  of  the  water,  remove  the  hand  or 
paper.  With  its  lower  end  dipping  about  6cm  below  the 


28  EXPERIMENTAL   PHYSICS. 

surface  of  the  water,  clamp  the  chimney  in  a  vertical 
position.  (Why  the  water  remains  in  the  chimney  you  will 
learn  from  Exp.  20.)  With  its  closed  end  downwards, 
and  about  6cm  below  the  surface  of  water,  clamp  the  other 
chimney  in  a  vertical  position.  Push  the  diaphragm  of 
the  gauge  about  8cm  below  the  surface  of  the  water. 
Sometimes  bringing  the  diaphragm  under  the  chimney 
filled  with  water,  as  shown  in  Fig.  12,  sometimes  under 
the  chimney  whose  closed  end  is  in  the  water,  and  at 
other  times  under  neither,  carefully  move  the  diaphragm 
about  in  the  same  horizontal  plane. 

Do  you  observe  any  change  of  pressure  in  going  from 
one  point  to  another  in  the  same  horizontal  plane  ? 

What  is  your  inference  ? 

As  you  moved  the  diaphragm  from  place  to  place,  the 
depth  of  water  over  it  was  sometimes  greater  and  some- 
times less.  How  many  different  depths  of  water  were 
there  ? 

PART  2.  Where  it  is  impossible  to  pass  along  a 
straight  line  from  one  point  to  another  in  the  plane. 

Directions.  Push  the  chimney  filled  with  water  down 
till  its  open  end  is  about  10cm  below  the  level  of  the 
water  in  the  pail.  Clamp  the  chimney.  Push  the  dia- 
phragm up  inside  the  chimney  about  2cm.  With  the 
marker  note  the  position  of  the  index.  Then,  with  the 
tube  bent  in  as  nearly  the  same  shape  as  before,  put  the 
diaphragm  in  the  water  outside,  but  on  a  level  with  its 
former  position  in  the  chimney.  Observe  the  position  of 
the  index.  Great  care  is  necessary  to  avoid  compressing 
the  rubber  tube. 


LIQUID   PRESSURE.  29 

In  this  part  of  the  experiment,  the  barrier  that  has 
separated  one  portion  of  the  horizontal  plane  from  the 
other  has  been  the  walls  of  the  chimney. 

What  inference  can  you  draw  ? 

EXAMPLES. 

1.  A  rectangular  vessel,  whose  interior  dimensions  are :  width  10cm, 
length  15cm,  and  height  20cm,  is  filled  with  water. 

a.    What  is  the  weight  of  water  in  the  vessel  ? 

6.  What  is  the  weight  of  water  resting  on  each  square  centimeter  of 
the  base  ? 

c.  What  is  the  pressure  upon  a  horizontal  square  centimeter  at  the 
depth  of  2cm  ?  At  a  depth  of  10cm  ?  At  a  depth  of  15cm  ? 

2.  Suppose  the  vessel  of  the  preceding  example  to  be  closed  by  a  flat 
cover  with  a  hole  through  its  center,  into  which  fits  an  open  tube  of 
Isq  cm  cross-section,  and  also  suppose  this  tube  to  extend  upwards  30cra 
above  the  top  of  the  vessel.     Suppose  both  vessel  and  tube  filled  with 
water. 

a.    What  is  the  total  weight  of  water  in  vessel  and  tube  ? 
6.    What  is  the  pressure  upon  that  square  centimeter  of  the  base  of 
the  vessel  which  lies  exactly  beneath  the  tube  ? 

c.  Is  the  pressure  upon  any  other  square  centimeter  of  the  base  of  the 
vessel  greater  or  less  than  this  ? 

d.  What  is  the  pressure  upon  that  square  centimeter  which,  at  the 
top  of  the  vessel,  lies  exactly  beneath  the  tube  ? 

e.  Is  the  pressure  against  each  square  centimeter  of  the  cover  greater 
or  Jess  than  this  ? 

/.    What  is  the  total  pressure  of  the  water  against  the  cover  ? 

ff.    What  is  the  total  pressure  of  the  water  against  the  base  ? 

h.  Subtract  the  total  pressure  against  the  cover  from  the  total  pressure 
against  the  base,  and  compare  the  result  with  the  weight  of  all  the  water 
in  the  vessel  and  tube. 

i.  What  is  the  total  pressure  upon  lsicm  of  the  vertical  side  of  the 
vessel,  the  center  of  the  square  being  at  a  depth  of  5cm  beneath  the 
cover  ?  At  a  depth  of  10cm  ?  At  a  depth  of  15cm  ? 


30  EXPERIMENTAL   PHYSICS. 

j.  What  is  the  total  pressure  upon  one  of  the  narrow  vertical  sides  of 
the  vessel  ?  Upon  one  of  the  broad  vertical  sides  ? 

k.   What  is  the  total  pressure  upon  the  base,  cover,  and  sides  ? 

I.  Suppose,  by  means  of  a  piston,  for  example,  a  pressure  of  50s  is 
brought  to  bear  upon  the  top  of  the  water  in  the  tube.  What  will  now 
be  the  pressure  upon  that  square  centimeter  which  lies  at  the  top  of  the 
vessel,  just  beneath  the  tube  ? 

m.  How  much  will  the  total  pressure  against  the  base  of  the  vessel  be 
increased  by  the  action  of  the  added  pressure  ? 

n.  How  much  will  the  total  pressure  against  the  base,  cover,  and 
sides  be  increased  by  the  action  of  the  added  pressure  ? 


ATMOSPHERIC    PRESSURE. 

14.  Pressure  of  the  Atmosphere.  In  Exp.  19  you 
found  that  the  lamp-chimney  remained  full  of  water  after 
it  was  inverted  in  the  pail  of  water.  In  the  following 
experiment  we  shall  study  the  cause  of  this. 

Experiment  2<X.  To  find  whether  it  was  the  pressure 
of  the  atmosphere  that  kept  the  water  in  the,  chimney. 

Apparatus.  In  place  of  the  chimney,  a  glass  tube  about  100cm 
long  and  0.5cm  in  diameter  ;  a  good  cork  stopple  to  fit  the  tube  ; 
a  pail  of  water. 

Directions.  With  the  stopple  close  one  end  of  the 
tube,  then  fill  it  with  water.  Taking  care  not  to  shut  in 
an  air-bubble,  press  the  finger  firmly  against  the  open  end. 
Place  the  end  covered  with  the  finger  under  the  surface 
of  the  water  in  the  pail  and  then  remove  the  finger. 

Does  the  water  in  the  tube  fall  ? 

When  you  remove  the  stopple,  what  is  the  result  ? 

Before  the  stopple  was  removed,  did  the  atmosphere 
get  to  the  water  in  the  tube  to  press  it  down  ?  Did  the 
atmosphere  get  to  the  water  in  the  tube  to  hold  it  up  ? 


ATMOSPHERIC   PRESSURE.  31 

If  the  atmosphere  did  not  get  at  the  water  in  the  tube 
directly  to  hold  it  up,  by  what  indirect  means  was  the 
pressure  of  the  atmosphere  transmitted  to  the  water  in  the 
tube  ?  What  inference  can  you  draw  ? 

15.     Precautions    to    be    taken  in    Using-    Mercury. 

It  would  bft  interesting  to  find  how  tall  a  column  of  water 
the  pressure  of  the  atmosphere  would  support ;  unfor- 
tunately, however,  a  tube  of  sufficient  length  for  the  water 
would  be  hard  to  manage ;  so  we  make  use  of  a  short  tube 
and  mercury,  a  liquid  much  heavier  than  water.  Mercury, 
or  quicksilver,  as  it  is  often  called,  has  a  specific  gravity 
of  13.6.  We  shall  use  mercury  in  several  experiments. 
The  vapor  of  mercury  is  poisonous,  hence  do  not  heat 
mercury  in  the  room.  Before  beginning  an  experiment 
in  which  mercury  is  used,  remove  rings  from  the  fingers, 
as  it  badly  stains  gold.  In  performing  experiments  with 
mercury,  place  all  the  apparatus  in  a  shallow  pan  to  catch 
any  mercury  accidentally  spilt. 

Experiment  21.  To  find  how  tall  a  column  of  mercury 
the  pressure  of  the  atmosphere  will  support. 

NOTE.  This  is  often  called  the  "  Torricellian  Experiment,"  in  honor 
of  Torricelli  (pronounced  tor-re-chel'lee),  an  Italian  who  performed  the 
experiment  in  1643. 

Apparatus.  A  piece  of  thick  glass  tube,  whose  bore  is  about 
0.6cm  in  diameter,  about  80cm  long,  closed  at  one  end  ;  a  retort-stand 
with  clamp  ;  an  iron  pan ;  a  small  mortar ;  a  small  funnel';  a  piece 
of  iron  wire  ;  a  piece  of  cloth  ;  mercury ;  a  meter  stick. 

Directions.  Make  a  soft  pad  of  the  cloth  and  lay  it 
in  the  pan.  On  the  pad  rest  the  closed  end  of  the  tube, 
and  clamp  in  a  vertical  position.  By  the  aid  of  the  funnel 
half  fill  the  tube  with  mercury;  then,  by  twisting  the 


32 


EXPERIMENTAL   PHYSICS. 


wire  in  the  tube,  remove  the  air-bubbles  which  adhere 
to  the  sides.  Add  a  little  more  mercury  and  again  remove 
any  air-bubbles  that  you  may  see.  When  the 'tube  is  com- 
pletely filled  with  mercury  and  contains  no 
air-bubbles,  have  ready  in  the  pan  the  mortal- 
filled  with  mercury  to  a  depth  of  about  3cm. 
Placing  the  finger  firmly  over  the  open  end, 
grasp  the  tube  near  the  top  with  the  right 
hand.  With  the  left  hand  unclamp  the  tube, 
grasp  it  near  the  bottom,  and  in- 
verting the  tube,  place  the  end  in 
the  mortar  below  the  level  of  the 
mercury.  Taking  care  that  no  air 
enters,  remove  the  finger  and  again 
clamp  the  tube  in  a  vertical  position, 
as  in  Fig.  13. 

What  happens  when  the  finger  is 
removed  ? 

Measure   the    distance    from    the 
level    of    the    mercury   in 
the  mortar  to   the   top  of 
the  column  of  mercury  in 
the  tube. 

What  relation  is  there  between  the  pressure  at  a  point 
on  the  surface  of  the  mercury  in  the  mortar  and  the  pres- 
sure at  a  point  on  the  same  level  in  the  mercury  in  the 
tube  ?  (See  your  inference  from  Exp.  19,  Part  2.) 

Experiment  22.  To  find  what  weight  of  mercury  in 
the  tube  the  atmospheric  pressure  holds  up. 

Apparatus.  The  same  as  that  used  in  Exp.  21 ;  a  glass  beaker : 
a  platform  balance. 


FIG.  13. 


ATMOSPHERIC   PRESSURE.  33 

Directions.  Using  the  same  care  as  in  Exp.  21,  fill 
the  tube  and  invert  it  in  the  mortar  partly  filled  with 
mercury.  When  the  top  of  the  mercury  column  has 
become  stationary,  find  its  height  as  in  the  last  experi- 
ment. Over  the  lower  end  of  the  tube  put  the  finger 
loosely,  and  gently  raise  the  tube  till  its  lower  end  is 
just  beneath  the  level  of  the  mercury.  Now  press  the 
finger  firmly  against  the  end  of  the  tube,  lift  the  tube 
out,  and  incline  it  in  a  nearly  horizontal  position.  By 
loosening  the  finger  admit  the  air,  a  few  bubbles  at  a 
time,  and  allow  the  mercury  to  run  very  gently  into 
the  beaker.  Do  not  spill  any  of  the  mercury.  Weigh 
the  beaker  with  the  mercury,  and  also  weigh  it  empty. 

What  weight  of  mercury  did  the  air  hold  up? 

In  taking  the  tube  from  the  mortar,  why  did  you  raise 
it  till  its  lower  end  was  just  beneath  the  surface  of  the 
mercury  before  pressing  firmly  with  the  finger  ? 

Making  use  of  the  height  and  weight  of  the  mercury 
column,  and  of  the  fact  that  the  specific  gravity  of  mer- 
cury is  13.6,  answer  the  following  questions  : 

What  was  the  volume  in  cubic  centimeters  of  the  mer- 
cury in  the  tube?  What  was  the  area  in  square  centi- 
meters of  the  cross-section  of  the  tube  ?  What  was  the 
pressure  in  grams  of  the  atmosphere  upon  an  area  of 
1S(1  cm  ?  What  would  be  the  length  in  centimeters  of  a 
column  of  water  supported  by  the  atmospheric  pressure? 

16.  The  Barometer.  The  barometer  is  an  instrument 
for  indicating  the  changes  in  the  pressure  of  the  atmos- 
phere. It  consists  of  a  cistern  filled  with  clean  mercury 
into  which  dips  an  upright  tube  of  glass  containing  mer- 
cury and  closed  at  the  upper  end ;  the  arrangement  is 


34  EXPERIMENTAL  PHYSICS. 

like  that  of  Exp.  21.  Alongside  the  tube  stands  a  scale 
to  measure  the  height  of  the  mercury  column.  By  watch- 
ing the  mercury  column  it  has  been  found  to  vary  in 
length  not  only  from  day  to  day,  but  frequently  also 
many  times  a  day.  This  shows  that  the  pressure  of  the 
atmosphere  is  sometimes  greater,  sometimes  less.  The 
pressure  of  the  atmosphere  is  expressed  by  the  length 
of  the  column  of  mercury  which  it  supports.  Thus,  if 
the  column  at  one  time  is  72cm  tall,  at  another  80cm,  we 
say  that  on  the  first  occasion  the  pressure  of  the  atmos- 
phere was  72cm,  on  the  other  80cm.  The  length  of  the 
mercury  column  is  called  the  height  of  the  barometer. 
The  average  height  of  the  barometer  at  the  sea  level 
is  about  76cm.  In  climbing  a  mountain  the  atmospheric 
pressure  becomes  less  and  less  the  higher  you  go,  so  if 
you  should  carry  a  barometer  from  the  base  to  the  top 
of  a  mountain,  the  height  of  the  column  of  mercury  would 
decrease.  The  space  above  the  mercury  in  a  barometer 
is  nearly  a  perfect  vacuum;  in  honor  of  Torricelli,  who 
first  observed  this,  it  is  called  a  Torricellian  vacuum. 
The  presence  of  the  vapor  of  mercury  in  this  space  pre- 
vents it  from  being  a  perfect  vacuum. 

The  term  "  barometric  pressure  "  is  often  used  in  place 
of  the  term  "  atmospheric  pressure." 

17.  Balancing-  Columns.  After  a  liquid  has  been 
poured  into  connecting  tubes  (Fig.  14),  the  column  of 
liquid  in  one  branch  is  said  to  balance  the  column  of 
liquid  in  the  other.  In  order  that  the  results  obtained 
in  experiments  with  balancing  columns  may  be  uninflu- 
enced by  the  capillary  action  (see  page  17),  the  branches 
of  the  connecting  tubes  must  be  sufficiently  wide  to  allow 


ATMOSPHERIC   PRESSURE.  35 

the  center  of  the  surface  of  the  liquid  in  each  column  to 
lie  flat. 

Experiment  23.  To  find  whether  two  balancing 
columns  of  water  contained  in  connecting  tubes  of 
unequal  cross-section  are  of  equal  height. 

Apparatus.  Two  connecting  tubes  of  glass 
of  unequal  cross-section,  as  shown  in  Fig.  14,  one 
about  0.5cm  in  diameter,  the  other  about  lcm. 

Directions.  Pour  water  into  the  larger 
tube. 

How  does  the  height  of  the  water  in 

FIG.  14. 

the  larger  tube  compare  Avith  the  height 
of  the  water  in  the  smaller? 

If  the  two  columns  of  Avater  are  of  the  same  height, 
Avhat  supports  the  extra  weight  of  the  -column  in  the 
larger  tube  ? 

Could  the  walls  of  the  tube,  where  they  narrow,  support 
this  weight  ? 

Experiment  24.  To  find  the  specific  gravity  of  a  liquid 
by  balancing  columns. 

Apparatus.  A  support  consisting  of  a  square  base  with  an 
upright  rod  about  100cm  long,  to  which  is  fastened  a  meter  stick  ; 
a  piece  of  rubber  tube  ;  two  glass  tubes,  each  about  100cm  long  and 
about  0.6cra  in  diameter  ;  a  funnel ;  a  beaker  ;  two  rubber  bands. 

Directions.  To  a  distance  of  about  lcm  over  an  end 
of  each  of  the  glass  tubes  slip  an  end  of  the  rubber  tube. 
Place  the  two  glass  tubes  parallel  to  each  other  so  that 
they  with  the  rubber  tube  look  like  a  very  tall  letter  U 
(we  shall  call  this  a  U-tube).  With  the  two  rubber  bands, 
as  shoAvn  in  Fig.  15,  one  near  the  top,  the  other  about 


36 


EXPERIMENTAL   PHYSICS. 


half  way  down,  firmly  fasten  the  U-tube  to  the  upright  of 
the  support.  Have  the  rubber  tube  so  bent  as  to  insure 
free  communication  between  the  two  branches.  In  order 

to  read  easily  the  level  of  the 
liquids,  have  a  branch  of  the 
U-tube  at  either  edge  of  the 
meter  stick. 

Into  one  branch  pour  water 
through  the  funnel  till  it  about 
half  fills  both.  By  drawing 
the  fingers  pressed  together 
along  the  rubber  tube,  drive 
out  any  hidden  air-bubbles. 
Into  one  of  the  branches,  very 
slowly  at  first,  pour  kerosene. 
Notice  the  well-defined  bound- 
ary between  the  kerosene  and 
the  water.  Continue  pouring 
kerosene  till  the  top,  &,  of  the 
column  of  kerosene  is  nearly 
on  a  level  with  the  top  of  the 
meter  stick.  Be  sure,  however,  that  the  boundary,  /,  be- 
tween the  kerosene  and  the  water  does  not  sink  out  of 
sight  into  the  rubber  tube. 

How  does  the  pressure  at  the  boundary  of  the  two  liquids 
compare  with  the  pressure  at  the  same  level  in  the  water  in 
the  other  tube  ?  (See  your  inference  from  Exp.  19,  Part  2.) 
How  does  the  weight  of  the  kerosene  column,  &/,  com- 
pare with  the  weight  of  the  water  column,  Iw,  which 
stands  above  the  horizontal  plane  passing  through  the 
boundary  of  the  kerosene  and  the  water  ? 


FIG.  15. 


ATMOSPERIC    PRESSURE.  37 

What  is  the  length  of  this  column  of  water  ? 

What  is  the  length  of  the  kerosene  column  ? 

How  does  the  weight  of  a  certain  length  of  the  kerosene 
column  compare  with  the  weight  of  an  equal  length  of 
the  water  column  ? 

What  is  the  specific  gravity  of  the  kerosene  ? 

QUESTION.  When  the  two  branches  of  a  U-tube  have  the  same  area 
of  cross-section,  suppose  a  column  of  water  80cm  tall  balances  a  column 
of  kerosene  100cm  tall ;  how  tall  a  column  of  kerosene  would  a  column 
of  water  80cm  tall  balance,  if  the  branches  of  the  U-tube  were  of  unequal 
area  of  cross-section  ? 

18.  Inverted  TJ-Tube.  Even  when  the  liquid  will 
mix  with  water,  the  method  of  balancing  columns  can  be 
used,  but  in  a  modified  form,  as  described  in  the  following 
experiment. 

Experiment  25.  To  find  the  specific  gravity  of  a  liquid 
by  means  of  the  inverted  U-tube. 

Apparatus.  The  support  and  the  glass  tubes  of  Exp.  24 ;  two 
small  tumblers  ;  a  lead  three-way  tube  ;  a  pinch-cock  ;  rubber 
tubing  ;  rubber  bands. 

Directions.  By  means  of  short  pieces  of  rubber  tube 
couple  a  glass  tube  to  each  of  the  parallel  arms  of  the 
three-way  tube.  Over  the  remaining  arm  .slip  a  somewhat 
longer  piece  of  rubber  tube,  which  is  clasped  loosely  by 
the  pinch-cock.  Fill  one  tumbler  with  water,  the  other 
with  kerosene,  and  place  them  side  by  side  upon  the  base 
of  the  support,  which  is  not  shown  in  Fig.  16.  To  this 
support  fasten,  in  an  inverted  position,  with  rubber  bands, 
the  U-tube  that  you  have  just  made,  with  one  of  the  glass 
tubes  dipping  into  the  water,  the  other  into  the  kerosene, 


38 


EXPERIMENTAL    PHYSICS. 


Record  the  height  to  which  capillary  attraction  raises 
the  liquids  in  each  tube.  Then  by  means  of  the  mouth 
draw  out  some  of  the  air  through 
the  rubber  tube  till  the  liquids 
rise  to  a  considerable  height  in 
each  tube,  and,  finally,  while  the 
liquids  are  raised  in  this  way, 
clamp  the  rubber  tube  with  the 
pinch-cock. 

Record  the  height  of  the  top  of 
each  column  of  liquid  above  the 
liquid  in  the  tumbler.  In  order 
to  find  the  heights  to  which  the 
liquids  actually  rose  by  reason  of 
removing  some  of  the  air  from 
the  tubes,  subtract  from  each  of 
the  recorded  heights  the  amount  of 
elevation  due  to  capillary  attrac- 
tion at  first  observed  in  each  tube. 
When  thus  corrected,  what  is  the 
true  height  of  the  water  column, 
and  of  the  kerosene  column  ? 

How  does  the  weight  of  a  certain 
length  of  the  kerosene  column  com- 
pare with  the  weight  of  an  equal 
length  of  the  water  column  ? 
What  is  the  specific  gravity  of  the  kerosene  ? 

SPECIFIC    GRAVITY    OP    AIR. 

19.     Specific     Gravity    of    Air.       We    have    become 
acquainted  with  methods  for  finding  the  specific  gravity 


FIG.  16. 


SPECIFIC    GRAVITY    OF    AIR. 


39 


of  solids  and  of  liquids.  In  the  following  experiment  we 
shall  get  the  specific  gravity  of  air  by  a  method  that  will 
serve  to  illustrate  roughly  the  way  in  which  the  specific 
gravity  of  gases  may  be  found. 

Experiment  26.      To  find  the  specific  gravity  of  air. 

Apparatus.  An  air-pump  of  simple  construction  (see  Fig.  19); 
a  dry  2-quart  bottle  with  a  perforated  rubber  stopple,  through  which 
is  thrust  a  piece  of  glass  tube  long  enough 
almost  to  touch  the  bottom  of  the  bottle 
and  to  project  about  2cm  above  the  stopple; 
a  piece  of  pressure  tube  about  30cm  long; 
a  brass  clamp ;  a  250CC  graduate  ;  a  glass 
jar  filled  with  water  ;  a  platform  balance. 

Directions.  Into  the  mouth  of 
the  bottle  insert  the  stopple  slightly 
smeared  with  vaseline  to  make  the 
bottle  air-tight.  Over  the  end  of 
the  glass  tube  outside  of  the  bottle 
slip  the  pressure  tube  and  put  the 
clamp,  as  shown  in  Fig.  17,  loosely 
over  the  tube. 

Weigh  the  bottle  carefully,  to- 
gether with  tubes,  stopple,  and 
clamp.  Lay  the  bottle  on  its  side  close  to  the  air- 
pump.  Over  the  exhaust  nozzle  of  the  pump  slip  the 
end  of  the  pressure  tube.  Make  strokes  of  the  pump  to 
the  number  of  20  or  40,  or  until  the  air  as  it  escapes 
from  the  pump  makes  a  short,  faint  hiss.  Close  to  the 
end  of  the  pressure  tube  next  to  the  air-pump  make 
the  clamp  fast.  Detach  the  bottle  and  weigh  it  carefully. 

What  weight  of  air  has  been  removed  ?     (If  less  than 


FIG.  17. 


40  EXPERIMENTAL   PHYSICS. 

0.7g  has  been  removed,  pump  out  some  more  air  and  weigh 
again.) 

Near  the  edge  of  the  table  place  the  bottle  and  the  jar 
of  water.  To  a  considerable  depth  beneath  the  surface 
of  the  water  plunge  the  end  of  the  pressure  tube  and 
loosen  the  clamp.  As  the  water  runs  in,  hold  the  bottle 
upright  at  the  edge  of  the  table  close  beside  the  jar.  By 
raising  or  lowering  the  bottle,  keep  the  surface  of  water  in 
it  on  the  same  level  with  the  surface  of  water  in  the  jar. 

When  the  clamp  was  loosened,  what  made  the  water 
rush  into  the  bottle?  When  the  water  stops  flowing 
into  the  bottle,  what  is  the  relation  between  the  pressure 
of  the  atmosphere  and  the  pressure  of  the  air  in  the  bottle  ? 
What  is  the  reason  for  your  answer  ? 

Clamp  the  end  of  the  pressure  tube  and  loosen  the 
stopple.  Then  raise  the  tube  into  a  vertical  position, 
loosen  the  clamp,  and  allow  the  water  in  the  tube  to  run 
into  the  bottle.  (Why  ?)  Now  find  how  many  cubic  centi- 
meters of  water  there  are  in  the  bottle  by  measuring  this 
water  with  the  graduate. 

How  many  cubic  centimeters  of  air  at  atmospheric 
pressure  have  been  removed  from  the  bottle  ? 

How  many  grams  does  this  air  weigh  ?  (See  answer  to 
question  as  to  weight  of  air  removed.) 

What  is  the  weight  of  an  equal  volume  of  water  ? 

What  is  the  specific  gravity  of  air  ? 

NOTE.     Keep  the  bottle  and  tubes  for  the  next  experiment. 

Experiment  27.  To  find  what  part  of 'the  air  contained 
in  the  bottle  was  removed. 

Apparatus.  The  bottle,  stopple,  and  tubes  used  in  the  last 
experiment ;  a  250CC  graduate. 


BOYLE'S  LAW.  41 

Directions.  Fill  the  bottle  brimful  of  water.  Into 
the  mouth  of  the  bottle,  holding  the  tube  upright,  put  the 
stopple,  and  press  it  into  place.  Then  remove  the  stopple, 
and  let  the  water  in  the  tube  run  into  the  bottle.  (Why?) 
With  the  graduate  find  how  many  cubic  centimeters  of 
water  there  are  in  the  bottle.  In  the  last  experiment  you 
found  the  number  of  cubic  centimeters  of  air  at  atmos- 
pheric pressure  removed. 

What  part  of  the  air  originally  in  the  bottle  was 
removed  ? 

The  quotient  just  found,  is  called  the  degree  of  exhaus- 
tion ;  hence  the 

Definition.  The  degree  of  exhaustion  is  a  number  that 
tells  what  part  of  the  air  contained  in  a  vessel  has  been 
removed.  This  numerical  value  is  expressed  as  per 
cent. 

QUESTION.  If  a  vessel  of  1000CC  capacity,  filled  with  air  at  atmos- 
pheric pressure,  has  950CC  taken  out,  what  is  the  degree  of  exhaustion  ? 

Ans.  95  per  cent. 

BOYLE'S    LAW. 

2O.  Boyle's  Law.  When  we  found  the  specific 
gravity  of  air,  we  made  no  account  of  the  height  of  the 
barometer.  The  specific  gravity  of  air  depends  on  the 
pressure  of  the  atmosphere;  so  it  will  be  interesting  to 
find  what  relation  there  is  between  the  pressure  of  the 
atmosphere  and  the  volume  occupied  by  a  portion  of  it. 
The  relation  is  known  as  Boyle's  Law.1 

1  In  honor  of  Robert  Boyle,  who  discovered  the  law  in  1662. 


42 


EXPERIMENTAL   PHYSICS. 


Experiment  28.  To  find  the  relation  between  the  volume 
of  a  certain  mass  of  air  and  the  pressure  put  upon  this  air. 

Apparatus.  A  wooden  support  like  the  one  used  in  Exp.  24  ; 
a  clean  Boyle's  tube  ;  clean  mercury  ;  a  medicine  dropper ;  two 
rubber  bands. 

Directions.  Fasten  the  tube  to  the  support  by  rubber 
bands  (Fig.  18).  Get  the  reading  of  the  barometer. 

Carefully  pour  mercury  into  the 
tube  till  the  bend  is  covered  and 
the  mercury  stands  about  3cm 
higher  in  the  long  arm  than  in 
the  short.  Tip  the  tube  to  al- 
low some  air  to  escape  from  the 
short  arm;  place  the  tube  up- 
right again  ;  note  the  levels  and, 
if  necessary,  repeat  the  tipping 
(in  the  opposite  direction  this 
time,  perhaps)  till  the  mercury 
in  the  closed  arm  stands  lcm  or 
2cm  above  the  level  of  the  mer- 
cury in  the  long  arm.  Then, 
by  means  of  the  medicine 
dropper,  cautiously  add  mercury 
till  the  two  levels  are  the  same. 
In  the  subsequent  parts  of  the 
experiment  the  tube  must  not 
be  tipped,  lest  the  air  in  the 
closed  arm  be  increased  or 

FIG.  18.  ,.     .    .  ,      , 

diminished. 

Be  sure  to  have  the  level  of  the  mercury  from  lcm  to  3cm 
above  the  curve  of  the  tube.  Read  and  record  the  posi- 


BOYLE'S  LAW.  43 

tion  of  the  top  of  the  meniscus,  or  rounded  part  at  the  end, 
of  each  mercury  column  above  the  base  of  the  support. 

What  is  now  the  pressure  on  the  air  in  the  closed  arm  ? 
[See  your  inference  from  Exp.  19,  Part  2.] 

Now  pour  in  some  more  mercury,  adding  the  mercury 
by  means  of  the  medicine  dropper,  globule  by  globule 
towards  the  last,  till  the  level  of  the  mercury  in  the  open 
arm  is  half  of  the  barometric  height  above  the  level  of  the 
mercury  in  the  short  arm. 

Record  the  heights  of  the  tops  of  the  columns  above  the 
base.  In  this  experiment  all  measurements  of  length 
must  be  recorded  in  centimeters. 

What  is  the  pressure  on  the  air  in  the  closed  branch 
now? 

Pour  more  mercury  into  the  tube  till  the  level  of  the 
mercury  in  the  open  arm  is  just  the  barometric  height 
above  the  level  of  the  mercury  in  the  short  arm.  Record 
the  heights  as  before. 

What  is  the  pressure  on  the  air  in  the  closed  arm  now  ? 

Finally,  if  the  tube  is  long  enough,  make  the  level  of 
the  mercury  in  the  open  arm  stand  one  and  one-half  times 
the  barometric  height  above  the  level  of  the  mercury  in 
the  closed  arm.  As  before,  record  heights. 

What  is  the  pressure  on  the  air  in  the  closed  arm  now  ? 

Get  the  reading  of  the  barometer  again.     (Why  ?) 

Measure  and  record  the  height  of  the  inside  of  the  top 
of  the  closed  arm  above  the  base  of  the  support. 

If  you  divide  each  of  the  last  three  pressures  in  your 
record  by  the  first  (the  atmospheric)  pressure,  you  can  put 
the  quotients  into  the  following  form 


44  EXPERIMENTAL   PHYSICS. 

As  the  tube  is  of  uniform  bore,  the  volume  of  air  in  the 
short  arm  is  proportional  in  each  case  to  the  length  of 
the  air  column  in  the  short  arm,  therefore,  divide  each 
of  the  last  three  lengths  by  the  first  and  the  quotients 
will  be  the  same  as  those  obtained  by  dividing  the  actual 
volumes.  Put  these  quotients  into  the  fractional  form 
and  see  how  nearly  they  agree  with 


From  the  results  obtained  by  comparing  the  quotients 
of  the  pressures  with  the  quotients  of  the  corresponding 
volumes,  what  do  you  find  to  be  the  relation  between  the 
volume  of  a  certain  quantity  of  air  and  the  pressure  put 
upon  this  air? 

What  keeps  the  mercury  from  filling  the  short  arm  ? 

What  principles  learned  in  previous  experiments  have 
you  made  use  of  in  this  ? 


EXAMPLES. 

1.  A  bent  .tube,  having  one  end  open  and  the  other  end  closed,  con- 
tains mercury  which  stands  60cm  higher  in  the  open  than  in  the  closed 
branch.  Compare  the  pressure  of  the  air  in  the  closed  branch  with  that 
of  the  external  air  ;  the  barometer  at  the  time  standing  at  75cm. 

Solution.  Since  the  pressure  is  equally  great  at  all  points  in  a  hori- 
zontal plane  passing  through  a  liquid  (see  your  inference  from  Exp.  19, 
Part  2),  the  pressure  at  the  surface  of  the  mercury  in  the  closed  branch 
(that  is,  the  pressure  of  the  confined  air)  must  equal  the  pressure  at  the 
same  level  in  the  open  branch  ;  but  the  pressure  at  this  level  in  the  open 
branch  is  the  pressure  due  to  the  column  of  mercury  60cm  high  plus  the 
pressure  due  to  the  external  air  bearing  down  upon  the  top  of  this  mer- 
cury column  ;  but  this  air  pressure  is  equal  to  75cm  (that  is,  it  will  support 
a  column  of  mercury  75cm  high)  ;  so  the  total  pressure  will  be 

60cm  4-  75cm  =  135cm. 


46 

Thus  the  pressure  of  the  mass  of  air  confined  in  the  closed  branch  is 
135'm. 

.-.  pressure  of  confined  air  :  pressure  of  external  air  =  135  :  75  =  9  :  5. 

That  is,  the  pressure  of  the  air  in  the  closed  branch  is  |  as  great  as 
that  of  the  external  air. 

2.  A  mass  of  air  occupies  100CC  when  the  pressure  is  60cm.     What 
volume  will  it  occupy  when  the  pressure  is  120cm  ? 

Solution.  Boyle's  Law  states  that  the  volume  of  a  gas  varies  inversely 
as  the  pressure ;  for  example,  if  a  mass  of  air  has  a  volume  V\  when  the 
pressure  is  PI  ,  and  a  volume  F2  when  the  pressure  is  P2 ,  we  shall  have 
the  following  relation  among  V\ ,  F2  5  PI  »  and  Pg  : 

Fi  :  Fa-=  P2  :  PI  ; 

or,  if  we  call  FI  the  first  volume,  F2  the  second  volume,  PI  the  first 
pressure,  and  P2  the  second  pressure,  we  shall  say 

1st  Volume  :  2nd  Volume  =  2nd  Pressure  :  1st  Pressure. 
In  the  special  problem  given  for  solution  we  have 

Fi  =  100,  PI  =  60, 

F2  =  x.  P2  =  120. 

So  100  :  x  =  120  :  60, 

120  x  =  6000, 
x-50. 

Hence  the  required  volume  will  be  50CC. 

3.  A  mass  of  air  occupies  200CC  when  the  pressure  is  76cm.     What 
must  the  pressure  be  in  order  that  this  mass  of  air  shall  occupy  only 
25CC? 

4.  In  performing  the  Torricellian  experiment,  an  inch  in  length  of  the 
tube  is  occupied  with  air  at  atmospheric  pressure  before  the  tube  is 
inverted.     After  the  inversion,  this  air  expands  till  it  occupies  15  inches, 
when  a  column  of  mercury  28  inches  high  is  sustained  below  it.     Find 
the  true  barometric  height. 

Solution.  In  the  statement  of  the  problem  nothing  is  said  about  the 
area  of  the  cross-section  of  the  tube,  so  we  cannot  find  the  volume  of  the 
air  that  fills  an  inch  in  length  of  the  tube  ;  but  let  us  denote  the  area  of 
this  cross-section  by  a,  then  a  will  denote  the  volume  of  the  air  in  cubic 


46  EXPERIMENTAL   PHYSICS. 

inches.  After  the  hi  version  of  the  tube,  15  a  will  denote  the  new  volume 
in  cubic  inches.  If  x  denotes  the  true  barometric  height,  that  is,  the 
pressure  of  the  atmosphere,  we  know,  as  was  stated  in  the  solution  of 
Example  1,  that  the  pressure  at  the  level  of  the  mercury  in  the  cup,  into 
which  the  tube  was  inverted,  is  equal  to  the  pressure  within  the  tube  on 
the  same  plane.  The  pressure  on  the  portion  of  the  plane  within  the 
tube  is  measured  by  the  height  of  the  mercury  column  above  it  plus  the 
pressure  of  the  confined  air  upon  the  top  of  this  column.  The  length  of 
this  mercury  column  is  given  in  the  statement  of  the  problem  as  28 
inches.  Let  us  denote  by  P%  the  pressure  of  the  confined  mass  of  air, 
then  the  pressure  on  the  portion  of  the  plane  within  the  tube  is  28  +  P%  ; 
but  this  has  just  been  shown  to  be  equal  to  the  atmospheric  pressure  x  ; 

hence  28  +  P2  -  x. 

.:P2=x-2S. 

Collecting  what  we  know  to  be  true  about  the  volumes  and  the 
pressures  in  this  problem,  we  have 


Hence,  by  Boyle's  Law, 

a  :  15  a  =  x  —  28  :  x, 
ax  =  15  a  (x  —  28), 
x  =  15  (x  -  28), 


Hence  the  true  barometric  height  is  30  in. 

NOTE.  It  will  be  seen  that  the  a,  which  we  introduced  for  the  purpose 
of  expressing  the  volume  of  the  air,  does  not  appear  in  the  result.  In 
other  words,  it  does  not  matter  what  the  area  of  the  cross-section  of  the 
tube  may  be. 

5.  A  tube  of  uniform  cross-section,  200cm  long,  closed  at  one  end,  is 
pushed  open-end  downward  into  a  deep  cup  of  mercury  till  the  air  within 
it,  which  originally  filled  the  whole  tube,  is  reduced  to  one-half  of  its  first 
volume.  The  barometer  at  the  time  of  performing  the  experiment  reads 
76cm.  How  far  below  the  surface  of  the  mercury  in  the  cup  is  the 
surface  of  the  mercury  in  the  tube  ?  How  far  is  the  closed  end  of  the 
tube  above  the  general  surface  of  the  mercury  in  the  cup  ? 


BOYLE'S  LAW.  47 

6.  A  quantity  of  air  is  collected  in  a  barometer  tube,  the  mercury 
standing  10  in.  higher  inside  the  tube  than  outside,  and  the  correct  baro- 
metric height  being  30  in.  If  the  volume  of  the  air  under  these  con- 
ditions is  1  cu.  in.,  what  would  be  its  volume  at  atmospheric  pressure  ? 

Solution.  Since  the  pressure  at  all  points  in  a  horizontal  plane  passing 
through  a  liquid  is  equally  great,  we  shall  have,  denoting  by  PI  the 
pressure  of  the  air  confined  in  the  tube, 

Pi  +  10  =  30. 

.-.  P!  =  20. 

Collecting  what  we  know  to  be  true  about  the  volumes  and  the 
pressures  in  this  problem,  we  have 

Fi  =  1,  P!  =  20, 

F2  =  x.  P2  =  30. 

Hence,  by  Boyle's  Law, 

1  :  x  =  30  :  20, 


The  required  volume  is,  then,  f  cu.  in. 

7.  A  quantity  of  air  occupying  10CC  is  admitted  to  the  space  above  the 
mercury  column  of  a  barometer,  and  there  expands  till  it  occupies  30CC. 
The  column  of  mercury  beneath  this  air  is  now  50cm  high.     How  high 
was  it  before  the  admission  of  the  air  ? 

SUGGESTION.  Denoting  by  x  the  required  height,  show  that  the 
pressure  of  the  air  in  the  tube  is  denoted  by  x  —  50.  Then  collect  what 
you  know  to  be  true  about  the  volumes  and  the  pressures,  and  apply 
Boyle's  Law. 

8.  The  tube  of  a  barometer  has  a  cross-section  of  lsqcm}  and  when  the 
mercury  column  stands  at  77cm,  the  length  of  the  empty  space  above  it 
is  8cm  ;  how  far  will  the  mercury  column  be  depressed  if  lcc  of  air  is 
passed  up  into  the  tube  ? 

Solution.  Suppose  the  mercury  to  be  depressed  through  xcm  •  then  if 
we  denote  by  P2  the  pressure  of  the  air  confined  in  the  tube,  we  shall 

have  77-z+P2  =  77. 

.-.  Po  =  X  ; 

that  is,  x  measures  the  pressure  of  this  air. 


48 


EXPERIMENTAL   PHYSICS. 


Since  the  cross-section  of  the  tube  is  ls(i  cm,  the  volume  of  this  air  is 

(X  +  8)cc. 

Collecting  what  we  know  to  be  true  about  the  volumes  and  the 
pressures  in  this  problem,  we  have 

Fi  =  1,  Pi  =  77, 

r2  =  x  +  s.  P2  =  x. 

By  Boyle's  Law,  we  have 

1  :x  +  8  =o;:77, 
(x  +  8)  x  =  77, 


£2+8x+  16  =  77  +  16, 
(x  +  4)2  =  93, 
x  +  4  =  9.65, 
x  =  5.66. 

Hence  the  mercury  column  is  depressed  through  5.65cm. 
9.   A  cylindrical  diving-bell,  9  ft.  high,  is  immersed  in  water  so  that 
its  top  is  27  ft.  below  the  surface.     If  the  height  of  the  water-barometer 
is  34  ft.  ,  find  how  high  the  water  rises  within  the  bell. 


21. 


PUMPS. 

The  Air-Pump.  We  have  already  used  in  the 
laboratory  (Exps.  14,  15,  and  25) 
an  air-pump  of  very  simple  con- 
struction. This  pump  consists 
(Fig.  19)  of  a  hollow  metallic 
cylinder,  (7,  closed  at  the  bottom, 
where  it  is  supported  in  a  vertical 
position  by  an  iron  foot  not  shown 
in  the  figure.  In  the  cylinder  is  a 
piston,  D,  which  fits  tightly,  but 
which  can  readily  be  pushed  down 
and  pulled  up  by  a  handle  at- 
tached by  the  rod,  F,  to  the 
piston.  At  the  lower  end  of  the  cylinder  are  two  nozzles, 


PUMPS.  49 

E  and  Cr.  When  the  piston  is  worked,  air  is  drawn  in 
through  one  of  these  nozzles  and  pushed  out  through  the 
other.  On  unscrewing  the  nozzles,  a  valve  will  be  found 
behind  each.  These  valves  are  made  of  thin  sheet-brass, 
and  are  conical  in  form.  They  fit  closely  into  conical 
holes  communicating  with  the  interior  of  the  cylinder. 
The  conical  holes  are  called  valve  seats.  In  one  nozzle 
the  valve  seat  tapers  towards  the  end  of  the  nozzle, 
while  the  valve  seat  behind  the  other  tapers  towards  the 
cylinder. 

If  the  vessel  from  which  the  air  is  to  be  taken  is  con- 
nected by  means  of  a  piece  of  thick-walled  rubber  tubing 
to  the  nozzle  covering  the  valve  whose  sharp  end  points 
outward,  and  the  piston  is  raised  by  pulling  up  on  the 
handle,  the  air  in  the  cylinder  expands,  and  thereby  its 
pressure  is  diminished ;  so  the  air  in  the  vessel  also 
expands,  and  rushes  into  the  cylinder  until  the  pressure 
becomes  equal  in  both.  When  the  piston  is  pushed  down, 
the  air  in  the  cylinder  is  compressed.  This  compressed 
air  closes,  by  pressing  into  its  seat,  the  valve  by  which  the 
air  entered  the  cylinder ;  but  it  opens  the  other  valve  and 
escapes  into  the  external  air.  By  repeating  the  process  of 
raising  and  lowering  the  piston,  more  air  is  taken  from 
the  vessel,  till,  finally,  the  difference  of  pressure  between 
the  air  in  the  vessel  and  the  air  in  the  cylinder  becomes 
so  small  that  it  is  unable  to  open  or  close  the  valve. 

No  air-pump  has  ever  been  made  that  will  give  a  perfect 
vacuum.  In  the  construction  of  air-pumps,  however,  such 
skill  and  ingenuity  have  been  used  that  with  a  good  pump 
one  may  obtain  a  nearly  perfect  vacuum.  The  bulbs  of 
incandescent  lamps  which  you  see  in  shops  and  houses 


50 


EXPERIMENTAL    PHYSICS. 


lighted  by  electricity  have  the  air  removed  from  them  by 
an  efficient  pump  of  peculiar  construction.  In  the  side 
and  near  the  top  of  a  long  upright  tube  is  an  opening  to 
which  the  lamp-bulb  is  attached  at  a  certain  stage  in  its 
process  of  manufacture.  Mercury  is  then  poured  down 
the  tube.  As  the  mercury  passes  the  opening,  the  air  in 
the  bulb  expands  and  is  swept  down  the  tube. 

22.    The    Common    Lifting- -  Pump.      This    pump,    so 
common  in  houses  and  yards,  is  used  for  raising  water 
from  a  well  or  cistern  to  the  surface 
of  the  ground.     The   construction  of 
this  pump  is  as  follows  : 

A  long  pipe,  A  (Fig.  20),  extends 
from  the  surface  of  the  ground  to  some 
distance  below  the  surface  of  the  water 
in  the  well.  At  its  upper  end  the  pipe 
has  a  valve,  J5,  hinged  like  a  trap-door, 
opening  upwards.  To  the  upper  end 
of  the  pipe  is  fastened  a  hollow  cylin- 
der, (7,  in  which  is  a  tightly  fitting 
piston,  D,  that  can  be  raised  and 
lowered  by  lowering  and  raising  the 
pump-handle  to  which  it  is  attached 
by  means  of  a  rod,  F.  In  the  piston  is 
a  valve,  6r,  opening  upwards  like 
that  in  the  pipe.  We  shall  explain 
the  action  of  the  pump  by  supposing  the  part  of  the  pipe 
above  the  water  in  the  well  to  be  filled  with  air  at  the 
start.  On  pushing  down  the  piston  by  raising  the  pump- 
handle,  the  air  in  the  cylinder  is  compressed.  This  com- 


FlG.  20. 


PUMPS.  51 

pressed  air  pushes  down  on  the  valve,  J9,  and  closes  it 
more  tightly  ;  but  by  pushing  up  on  the  valve,  6r,  in  the 
piston,  the  compressed  air  opens  it,  and  continues  to 
escape  as  long  as  the  piston  descends.  When  the  piston 
is  raised,  the  air  in  the  cylinder  becomes  rarefied  ;  the 
atmosphere  presses  down  on  the  valve  in  the  piston  and 
closes  it  tightly,  but  the  air  in  the  tube  pushes  open  the 
valve,  B,  and  enters  the  cylinder.  By  again  lowering 
the  piston  and  raising  it,  some  more  air  is  taken  out.  In 
the  meantime  the  pressure  of  the  atmosphere  on  the  water 
in  the  well  forces  the  water  up  the  tube,  till,  as  the  action 
of  the  pump  is  continued,  the  water  enters  the  cylinder. 
Now,  when  the  piston  is  pushed  down,  the  water  rises 
through  the  piston-valve,  6r  ;  when  the  piston  is  raised 
again,  the  piston-valve  closes,  and  the  valve  in  the  pipe  is 
pushed  open  by  the  water  forced  into  the  cylinder  by  the 
pressure  of  the  atmosphere.  The  piston  lifts  the  water 
above  it  until  the  spout  is  reached,  whence  the  water  flows 
into  the  pail  placed  to  receive  it.  Each  succeeding  stroke 
brings  a  fresh  supply  of  water,  which  keeps  a  nearly  con- 
tinuous stream  flowing  from  the  spout. 

It  frequently  happens  that  the  valves  do  not  fit  accu- 
rately, and  in  such  cases  it  is  necessary,  in  starting  the 
pump,  to  pour  some  water  into  the  cylinder  above  the 
piston. 

QUESTION.  When  the  mercury  barometer  column  stands  at  a  height 
of  30  inches  (specific  gravity  of  mercury  =  13.6),  what  is  the  greatest 
height  to  which  water  can  be  raised  by  the  common  lifting-pump  ? 

23.  The  Force-Pump.  This  is  the  pump  employed 
when  water  is  to  be  raised  to  a  height  above  the  pump,  or 
when  a  forcible  stream  is  desired.  In  construction  this 


52 


EXPERIMENTAL    PHYSICS. 


pump  resembles  the  lifting-pump,  but  the  piston,  instead 
of  having  a  valve  in  it,  is  solid ;  and  a  valve,  (7,  is  placed 
at  the  mouth  of  a  pipe  that  leads  from  a  point  near  the 
bottom  of  the  cylinder  to  the  place  where  the  water  is  to 
be  delivered.  The  valve,  B,  at  the  top  of  the  pipe  is 
placed  in  the  same  position  as  the  corresponding  one  in 
the  lifting-pump.  The  valve  in  the 
pipe  leading  from  the  side  of  the 
cylinder  opens  away  from  the  cylin- 
der (Fig.  21)  ;  consequently,  when 
the  piston  is  raised,  this  valve  closes 
(Why  ?),  and  the  air  below  the  valve, 
jB,  in  the  pipe  leading  into  the  well 
forces  its  way  through  and  rushes 
into  the  cylinder  to  equalize  the 
pressure.  By  continuing  the  pro- 
cess of  pumping,  the  air  is  at  last 
removed  from  the  pipe,  and  the 
water  in  the  well  is  forced,  by  the 
atmospheric  pressure  on  the  surface 
of  the  water  in  the  well,  into  the 
FlG  21  cylinder ;  then  the  piston,  when 

lowered,  pushes  down  on  this  water 
and  forces  it  through  the  valve,  6r,  into  the  side-pipe  ; 
when  the  piston  is  again  lifted,  more  water  is  raised  from 
the  well  into  the  cylinder.  (Why  does  not  the  water  that 
has  just  been  forced  into  the  side-pipe  run  back  into  the 
cylinder?)  Then,  lowered  again,  the  piston  forces  the 
water  in  the  cylinder  into  the  side-pipe,  which  conveys 
the  water,  as  the  pumping  goes  on,  to  the  place  where 
it  is  to  be  delivered. 


THE    SIPHON. 


53 


In  the  steam  fire-engine  and  other  force-pumps  the 
side-tube  leads  into  a  reservoir  of  air  ;  the  air  becomes 
somewhat  compressed  by  the  water  and  sends  it  out  in  a 
continuous  stream. 


THE    SIPHON. 

24.  The  Siphon.  The  siphon  (Fig.  22)  in  its  simplest 
form  is  a  bent  tube  open  at  both  ends.  It  is  used  for 
transferring  a  liquid  from  one  vessel  to  another  when  it  is 
not  convenient  to  make  .a  hole  in 
the  side  of  the  vessel  or  to  tilt  it  so 
that  the  liquid  shall  run  out.  To 
make  the  siphon  begin  working,  one 
end  is  dipped  into  the  liquid  which 
we  wish  to  remove,  and  suction,  by 
means  of  the  mouth  or  otherwise, 
is  applied  to  the  other  end.  When 
the  liquid  is  corrosive,  like  a  strong 
acid,  the  method  of  procedure  should 
be  to  fill  the  siphon  with  some  of 
the  liquid,  close  one  end,  and  dip 
the  other  into  the  vessel  of  liquid; 
on  uncovering  the  end,  the  liquid  will  at  once  begin  to 
flow.  In  order  that  the  siphon  may  work,  it  is  necessary, 
if  the  liquid  is  discharged  into  the  air,  that  the  end,  A, 
from  which  the  liquid  flows  should  be  below  the  level, 
EF,  of  the  liquid  in  the  vessel,  or,  if  the  liquid  is  dis- 
charged into  another  vessel,  the  surface  of  the  liquid  in 
this  vessel  must  be  at  a  lower  level  than  that  in  the 
former. 


FIG.  22. 


54  EXPERIMENTAL    PHYSICS. 

The  explanation  of  the  action  of  the  siphon,  the  reason 
why  the  liquid  flows  first  up  hill,  from  E  to  D,  and  then 
down  hill,  from  D  to  A,  is  as  follows  : 

The  pressure  inside  the  arm,  DA,  of  the  siphon,  which 
does  not  dip  into  the  vessel  containing  the  liquid  to  be 
removed,  at  a  point,  F,  lying  in  the  same  plane  as  the 
surface  of  the  liquid,  is  the  same  as  at  the  point,  E,  cor- 
respondingly situated  in  the  other  arm ;  but  this  pressure 
is  the  same  as  the  atmospheric  pressure  at  a  point  on  the 
surface  of  the  liquid  in  the  vessel  (Why  ?  See  your 
inference  from  Exp.  19,  Part  2).  The  pressure  of  the 
liquid  at  the  extremity,  A.,  of  the  arm  which  is  out- 
side the  vessel  is  greater  than  at  the  point,  F,  already 
spoken  of,  lying  on  a  level  with  the  surface  of  the  liquid 
(Why  ?  See  your  inference  from  Exp.  17) ;  but  the  pres- 
sure at  this  point  has  already  been  shown  to  be  equal  to 
the  atmospheric  pressure ;  hence  the  pressure  at  the 
extremity,  A,  of  the  tube  is  greater  than  the  atmospheric 
pressure,  and,  consequently,  the  liquid  pressure  at  this 
point  overcomes  the  atmospheric  pressure  from  without, 
and  the  liquid  tends  to  separate  at  the  highest  point,  D, 
of  the  siphon  and  to  run  out.  If  the  height  of  the  bend, 
.Z),  of  the  siphon  above  the  level  of  the  liquid  in  the  vessel 
is  less  than  the  height  at  which  the  liquid  would  stand  in 
a  barometer  tube,  the  pressure  of  the  air  will  prevent  the 
liquid  from  separating  at  the  bend,  D,  and  by  forcing 
the  column  of  liquid  to  ascend  in  the  arm  dipping  into 
the  liquid,  will  maintain  a  continuous  flow. 

How  long  will  the  liquid  continue  to  flow  after  the  level 
of  the  liquid  in  the  vessel  into  which  the  siphon  discharges 
becomes  the  same  as  that  of  the  liquid  in  the  first  vessel  ? 


THE    HYDROSTATIC    PRESS. 


55 


QUESTIONS.  When  the  barometer  stands  at  a  height  of  76cm,  what  is 
the  greatest  height  over  which  mercury  can  be  carried  by  means  of  a 
siphon  ?  When  the  barometer  stands  at  a  height  of  30  inches  (specific 
gravity  of  mercury  =  13.6),  show  by  computation  that  the  greatest  height 
over  which  a  siphon  can  raise  water  will  not  exceed  34  feet. 


THE    HYDROSTATIC    PRESS. 

25.    The  Hydrostatic  Press.     The  hydrostatic,  or,  as 
it  is  sometimes  called,  the  hydraulic  press,  is  a  machine 


FIG   23. 

for  lifting  heavy  weights,  and  for  compressing  merchan- 
dise into  small  compass.  This  machine  is  in  its  essential 
principles  constructed  as  follows  : 

Two  hollow  cylinders,  A  and  B  (Fig.  23),  of  iron,  each 
closed  at  one  end,  are  set  side  by  side  in  a  vertical  position 
with  their  open  ends  uppermost ;  a  pipe,  (7,  of  iron  con- 
nects the  two  near  the  bottom,  so  that  water  poured  into 
one  cylinder  will  flow  through  this  pipe  into  the  other. 
These  cylinders  are  of  unequal  area  of  cross-section,  the 


56  EXPERIMENTAL    PHYSICS. 

larger  being,  perhaps,  1000  times  that  of  the  smaller. 
From  Exp.  23,  you  already  know  that  if  water  is  poured 
into  one  of  the  cylinders  this  water  will  rise  to  an  equal 
height  in  both.  If  a  pressure  be  applied  by  means  of  a 
tightly  fitting  piston  to  the  top  of  the  water  column  in 
the  smaller  cylinder,  it  will  take  a  much  greater  pressure 
applied  to  the  top  of  the  water  column  in  the  larger  to 
balance  this  pressure;  thus,  if  a  pressure  of  1  Ib.  were 
applied  to  the  piston  of  the  smaller  cylinder,  a  pressure  of 
1000  Ibs.  would  have  to  be  laid  on  the  piston,  Z>,  that  rests 
on  the  top  of  the  water  column  in  the  larger  cylinder. 
The  explanation  of  this  fact  is  that  water  transmits  a 
pressure  applied  to  it  with  undiminished  force  in  all 
directions  ;  so  that  when  the  pressure  of  1  Ib.  is  applied 
to  the  top  of  the  smaller  water  column,  the  water  trans- 
mits this  pressure  to  each  portion  of  the  inner  surface  of 
the  two  cylinders  ;  consequently  each  portion  of  an  area 
equal  to  that  of  the  smaller  piston  has  now  upon  it  an 
additional  pressure  of  1  Ib.  As  the  area  of  the  face  of  the 
larger  piston  is  1000  times  that  of  the  smaller,  the  pressure 
on  this  face  will  be  1000  Ibs.  The  larger  piston  is  then 
forced  upwards  with  a  pressure  of  1000  Ibs.  Hence,  to 
keep  the  larger  piston  from  moving  up,  it  would  have  to 
be  loaded  with  a  weight  of  1000  Ibs. 

A  strong  framework  is  built  above  the  larger  cylinder, 
and  the  substance  that  is  to  be  compressed  is  put  between 
this  and  the  piston.  Had  the  area  of  the  cross-section  of 
the  larger  cylinder  been  10,000  times  the  area  of  the  cross- 
section  of  the  smaller,  a  pressure  of  1  Ib.  applied  to  the 
smaller  piston  would  produce  a  pressure  of  10,000  Ibs.  on 
the  larger  piston. 


MARIOTTE  S    BOTTLE. 


57 


The  hydraulic  press  is  widely  used  in  the  arts.  It  may 
be  constructed  to  give  pressures  of  two  or  three  hundred 
tons. 

MARIOTTE 'S    BOTTLE. 

26.  Mario tte's  Bottle.  This  piece  of  apparatus  (Fig. 
24)  consists  of  a  bottle  having  three  small  holes  drilled 
through  its  sides,  one  near  the  top,  one 
near  the  bottom,  and  the  third  half-way 
between  the  other  two.  A  rubber 
stopple  with  one  hole  has.  a  glass  tube 
thrust  through  it ;  this  tube  is  long 
enough  to  reach  to  the  bottom  of  the 
bottle  when  the  stopple  is  put  in  place, 
and  also  to  project  10cm  above  the  top 
of  the  stopple.  This  piece  of  apparatus 
is  very  useful  in  fixing  the  student's 
ideas  about  liquid  pressure  and  its  con- 
sequences ;  so  the  following  experiment 
should  be  carefully  performed. 


Experiment  29.      To  find  what  will 
7  .  7  FIG.  24. 

happen  on  removing  one  or  more  stopples 

in  the  side  of  a  Mariotte's  bottle  filled  with  water. 
Apparatus.     A  Mariotte's  bottle  ;  water. 

Directions.  After  securely  stopping  the  holes  in  its 
sides  by  means  of  small  cork  stopples,  as  shown  in  Fig.  24, 
fill  the  bottle  brimful  of  water ;  then  push  the  tube  and 
stopple  into  place  so  that  the  water  will  rise  in  the  tube 
and  stand  at  some  distance  above  the  stopple.  Be  careful 
not  to  have  any  air-bubbles  in  the  bottle. 


58  EXPERIMENTAL    PHYSICS. 

Before  removing  any  of  the  side  stopples,  as  you  will  be 
directed  to  do,  call  to  mind  the  facts  you  have  already 
learned  about  liquid  pressure  in  Exps.  17,  18,  and  19, 
and  try  to  predict  what  will  take  place  ;  then,  having 
made  up  your  mind  as  to  what  will  take  place,  remove 
the  stopple,  and  see  if  your  prediction  is  verified. 

After  placing  a  vessel  to  catch  the  water,  take  out  the 
stopple  that  closes  the  hole,  A,  highest  up  in  the  side  of 
the  bottle ;  then  replace  this  stopple  and  remove  the  one 
at  B ;  finally  replace  the  stopple  at  B  and  remove  the  one 
at  0. 

Does  the  water  run  out  freely  in  every  case  ? 

At  what  level  does  the  water  in  the  tube  stand  after  the 
removal  of  each  stopple  ? 

Now,  without  removing  the  large  stopple,  slip  the  tube  up 
till  its  lower  end  is  on  a  level  with  A ;  open  A  and  allow 
all  the  water  that  will  run  out  to  do  so.  Refill  the  bottle, 
push  the  tube  down  till  its  lower  end  is  on  a  level  half 
way  between  A  and  B,  and  remove  the  stopple  from  A ; 
then  close  A  and  let  the  water  run  from  B  a  short  time. 
Push  the  tube  down  till  its  lower  end  is  on  a  level 
between  B  and  C ;  have  the  bottle  completely  filled  with 
water  and  remove  the  stopple  at  A.  Replace  the  stopple 
at  A  and  remove  the  one  at  B.  Replace  the  stopple 
at  B  and  remove  the  one  at  O. 

In  order  to  have  water  flow  freely  from  the  bottle,  what 
relation  must  there  be  between  the  position  of  the  hole 
from  which  the  flow  takes  place  and  the  end  of  the  tube  ? 

Fill  the  bottle  once  more,  and  keeping  the  end  of  the 
tube  below  C  remove  the  stopple  at  (7,  and  then  take  out 
also  the  stopple  at  A. 


GRAPHICAL   METHOD.  59 

When  both  stopples  are  out,  what  takes  place  at  0? 
When  both  stopples  are  out,  what  takes  place  at  A  ? 
Write  out  a  brief  explanation  of  the  facts  you  have 
observed. 

GRAPHICAL    METHOD. 

27.    Graphical  Method  of  Representing  Results.     In 

Exp.  28  we  obtained  a  series  of  volumes  of  air,  which 
decreased  in  proportion  as  we  increased  the  pressure 
applied  to  the  confined  mass  of  air.  Whenever,  as  in 
this  instance,  we  have  a  series  of  results  which  depends 
on  a  uniform  variation  of  some  one  circumstance  in  the 
experiment,  the  relation  among  the  results  can  be  clearly 
represented  to  the  eye  by  employing  what  is  known  as 
the  graphical  method.  To  illustrate  the  application  of 
this  method,  let  the  following  be  the  data  obtained,  as 
in  Exp.  28  : 

PRESSURE.  VOLUME. 

1  100CC 
1.5  66.6 

2  50 
2.5  40 

3  33.3 
3.5  28.6 

4  25 

The  first  column  gives  in  atmospheres  the  pressures, 
which  have  been  increased  by  the  addition  of  half  an 
atmosphere  at  a  time ;  the  second  column  gives  the 
volume  corresponding  to  each  pressure. 


60 


EXPEEIMENTAL    PHYSICS. 


On  a  sheet  of  coordinate  paper,  which  is  ruled  into  little 
squares  by  equally  spaced  lines,  a  horizontal  line  is  chosen 


50 


40 


30 


20 


10 


10 


20 

PRESSURES. 

FIG.  25. 


30 


-40 


as  the  "  axis  of  abscissae,"  and  a  vertical  line  as  the  "  axis 
of  ordinates  ";  the  point  at  which  these  two  lines  intersect 
is  called  the  "  origin."  Starting  from  the  origin,  there  is 


GRAPHICAL   METHOD.  61 

laid  off  on  the  horizontal  line  a  certain  distance,  equal, 
say,  to  10  of  the  divisions,  as  in  Fig.  25,  to  represent  the 
first  pressure,  and  from  the  point  thus  reached  a  vertical 
distance  is  measured,  equal,  say,  to  50  of  the  divisions,  to 
represent  the  corresponding  volume  ;  the  end  of  this 
vertical  line  is  marked  by  a  point.  Each  of  the  remaining 
observations  is  treated  in  the  same  way  as  the  first,  by 
using  the  same  scale  as  was  at  first  employed  for  measur- 
ing distances  in  each  of  the  directions  (that  is,  if  10 
divisions  represent  1  atmosphere,  15  divisions  represent 
1.5  atmospheres  ;  if  50  divisions  represent  100CC,  33.3 
divisions  represent  66.6CC).  Finally,  a  strip  of  hard  rubber 
or  a  steel  spring  is  laid  edgewise  upon  the  paper,  and 
made  to  pass  through  the  points  marking  the  extremities 
of  the  vertical  lines.  A  line  is  drawn  through  these 
points  with  a  sharp  lead-pencil. 

This  line  represents  to  the  eye  the  relation  existing 
among  the  various  observations.  When  the  numerical 
data  employed  in  the  construction  of  this  line  have  been 
carefully  determined,  and  the  line  itself  drawn  with  pre- 
cision, it  is  possible  to  obtain  with  ease  and  accuracy  the 
volume  the  air  will  occupy  for  any  given  pressure  between 
the  extreme  pressures  made  use  of  in  this  experiment. 
To  do  this,  count  from  the  origin  on  the  horizontal  line  a 
number  of  divisions  corresponding  to  the  given  pressure  ; 
then  count  the  number  of  divisions  in  the  vertical  line 
lying  between  this  point  and  the  line  joining  the  extremi- 
ties of  the  vertical  lines.  The  number  thus  obtained  will 
represent  the  required  volume  on  the  scale  employed  in 
representing  the  volumes  ;  in  the  present  case  two  divi- 
sions on  a  vertical  line  represent  unit  volume. 


62  EXPERIMENT AL   PHYSICS. 

Let  the  student  construct  on  a  piece  of  coordinate  paper 
a  curve  in  the  manner  just  described,  using  the  results 
obtained  in  Exp.  28. 

EXPERIENCE. 

28.  Experience  ;  Observation  ;  Experiment.  At  this 
stage  of  our  progress  it  may  be  well  for  us  to  think  a  little 
about  the  first  thing  necessary  for  the  successful  study  of 
physics.  This  necessary  thing  is  experience,  which  fur- 
nishes us  with  facts.  We  obtain  experience  by  either 
observation  or  experiment. 

In  observation  we  merely  note  and  record  phenomena 
(that  is,  things  which  appear).  Thus,  a  U.  S.  Signal 
Service  man  observes  the  ever-changing  weather,  and 
notes  the  height  of  the  barometer,  the  temperature  and 
moisture  of  the  air,  the  direction  and  force  of  the  wind, 
the  height  and  character  of  the  clouds. 

In  experiment  we  vary  at  will  the  conditions  under 
which  phenomena  occur.  We  might  have  to  wait  years, 
or  even  centuries,  to  meet  with  facts  which  we  can  readily 
produce  at  any  moment  in  a  laboratory. 

The  work  of  the  U.  S.  Signal  Service  man  is  confined 
to  pure  observation,  for  he  is  unable  to  control  any 
of  the  phenomena  that  he  studies.  The  work  of  the 
physicist  and  the  chemist  is  not  confined  to  observation 
alone  ;  it  also  includes  experiment,  for  each  is  able  to  vary 
at  will  the  conditions  under  which  many  of  the  phenomena 
that  he  studies  occur.  Where  it  can  be  employed,  experi- 
ment is  a  fruitful  and  direct  means  of  getting  facts. 

Experiments  are  of  two  classes  :  qualitative  and  quanti- 
tative. 


EXPERIENCE.  63 

A  qualitative  experiment  has  for  its  object  the  production 
and  observation  of  phenomena. 

A  quantitative  experiment  has  for  its  object  the  measure- 
ment of  the  magnitudes  of  the  phenomena  produced. 

Exp.  19  is  a  qualitative  experiment ;  Exp.  21  is  a 
quantitative  experiment.  Divide  the  29  experiments  you 
have  performed  into  qualitative  and  quantitative  experi- 
ments, and  make  a  list  of  each  group. 

29.  Facts  and  Inferences  from  Facts.  On  the  left- 
hand  page  of  his  note-book  the  beginner  must  constantly 
try  to  record  only  what  his  senses  have  actually  observed. 
He  is  apt  to  record  his  own  character  and  feelings  rather 
than  the  facts,  for  the  mind  is  like  an  uneven  mirror,  and 
does  not  reflect  the  facts  without  distortion.  Since  the 
mind  by  long  experience  has  acquired  the  power  of 
judging  unconsciously  of  many  things  of  which  his  senses 
have  not  actually  assured  him,  the  beginner  confuses  facts 
observed  with  inferences  from  these  facts. 

EXAMPLES. 

1.  Find  the  specific  gravity  of  a  body  that  weighs  58s  in  air  and  40s  in 
water. 

2.  A  specific  gravity  bottle  holds  100s  of  water  and  180s  of  sulphuric 
acid.     Find  the  specific  gravity  of  the  acid. 

3.  Find  the  volume  of  a  solid  that  weighs  357s  in  air  and  253s  in 
water. 

4.  A  glass  ball  loses  33s  when  weighed  in  water,  and  loses  6s  more 
when  weighed  in  a  saline  solution.     Find  the  specific  gravity  of  the 
solution. 

5.  A  body  lighter  than  water  weighs  102s  in  air ;  and  when  it  is 
immersed  in  water  by  the  aid  of  a  sinker,  the  joint  weight  is  23s.     The 
sinker  alone  weighs  50s  in  water.     Find  the  specific  gravity  of  the  body. 


64  EXPEKIMENTAL   PHYSICS. 

6.  Find  the  specific  gravity  of  kerosene  from  the  following  data :  In  a 
U-tube  the  length  of  the  kerosene  column  is  100cm,  and  the  length  of  the 
water  column  just  balancing  this  is  79cm. 

7.  Find  the  volume  of  a  solid  which  weighs  458s  in  air,  and  409s  in 
brine.     Specific  gravity  of  the  brine  =  1.2. 

8.  How  much  weight  will  a  body  lose  whose  volume  is  47CC,  when 
weighed  in  a  liquid  the  specific  gravity  of  which  is  2.5  ? 

9.  How  much  water  will  1000CC  of  oak  displace  when  floating  in  equi- 
librium ?     Specific  gravity  of  oak  =  0.8. 

10.  Why  is  it,  in  the  metric  system  of  weights  and  measures,  that  the 
specific  gravity  of  a  substance  and  the  numerical  value  of  its  density  are 
the  same  ? 

11.  Define  density ;  define  specific  gravity.     A  certain  solid  floats  in 
water  with  only  two-thirds  of  its  volume  submerged.    What  is  the  specific 
gravity  of  this  solid  ? 

12.  A  pump  is  used  to  draw  water  from  a  well  through  a  vertical  pipe. 
How  long  may  the  pipe  be,  the  barometer  reading  76cm,  and  the  specific 
gravity  of  mercury  being  13.6  ?    Tell  and  explain  what  would  happen  if 
a  small  hole  were  bored  in  the  side  of  the  pipe,  when  full  of  water,  at  a 
point  half-way  up. 

13.  When  the  height  of  the  column  of  mercury  (sp.  gr.  =  13.6)  in  the 
barometer  is  80cm,  how  tall  a  column  of  water  can  the  pressure  of  the 
atmosphere  support  in  a  tube  having  a  perfect  vacuum  at  the  top  ? 

14.  A  rectangular  block  10cm  thick  floats  in  water  with  6cm  of  its 
depth  submerged.     Find  the  specific  gravity  of  the  block,  showing  your 
reasoning. 

15.  From  the  following  data  find  the  specific  gravity  of  sulphuric 
acid  : 

Weight  of  bottle  empty  =  5Qg. 

Weight  of  bottle  filled  with  water  =  150s. 

Weight  of  bottle  filled  with  sulphuric  acid  =  234s. 

16.  How  much  would  the  result  obtained  in  the  last  example  have 
been  changed  if  lcc  of  the  bottle  had  been  left  empty  when  it  was  weighed 
with  water  ? 

17.  A  cork  of  sp.  gr.  0.25,  the  volume  of  which  is  10CC,  floats  upon 
mercury  of  sp.  gr.  13.6.     How  great  is  the  submerged  part  of  the  cork  ? 

18.  Given  that  a  body  appears  by  the  indications  of  a  spring  balance 
to  weigh  15s  in  air  and  10s  in  water.     Answer  the  following  questions : 


EXAMPLES.  65 

(a)  If  the  balance  is  correct,  what  is  the  specific  gravity  of  the  body  ? 

(b)  If  each  reading  of  the  balance  is  only  T9o  as  large  as  it  should  be, 
what  is  the  specific  gravity  of  the  body  ? 

19.  A  cubical  vessel,  each  side  of  which  is  10cm  square,  has  a  tube 
Isqcm  m  cross-section  and  20cm  tall  rising  from  the  middle  of  its  top. 
The  tube  is  open  at  both  ends,  and  both  vessel  and  tube  are  full  of  water. 
Neglecting  atmospheric  pressure  and  weight  of  vessel  and  tube,  find 

(a)  The  total  pressure  which  the  vessel  and  tube  as  now  filled  exerts 
upon  the  support. 

(6)  The  total  pressure  exerted  against  the  bottom  of  the  vessel  by  the 
water  within  it  and  the  tube. 

If  the  pressures  are  not  equal,  explain  the  difference. 

20.  A  vessel  is  filled  with  water  to  a  depth  of  40cm.     A  cylinder  of 
wood  30cm  long  and  ICKH  cm  in  area  of  cross-section,  the  specific  gravity 
of  which  is  0.5,  extends  upward  through  a  hole  in  the  bottom  of  the 
vessel,  the  top  of  the  cylinder  being  20cm  beneath  the  surface  of  the 
water.     Show  whether  the  cylinder  tends  to  rise  or  fall,  and  how  great  a 
force  is  required  to  hold  it  in  its  present  position. 

21.  A  block,  the  density  of  which  is  to  be  determined,  is  measured 
with  a  scale  the  divisions  of  which  are  only  T%  as  long  as  they  are  sup- 
posed to  be.     How  much  too  small  or  too  large  will  the  value  found  for 
the  density  be  in  consequence  of  this  error  ? 

Solution.  Let  a,  6,  and  c  denote  the  true  dimensions  of  the  block, 
and  let  W  denote  its  weight.  Then  the  true  density,  d,  will  be 


abc 

As  each  of  the  divisions  of  the  faulty  scale  with  which  the  block  is 
measured  is  T9T  of  what  it  is  supposed  to  be,  that  dimension  of  the  block 
denoted  by  a  will,  according  to  this  scale,  have  a  value  equal  to  the 
number  of  times  a  contains  T%  ,  that  is, 


• 

In  like  manner,  the  dimension  denoted  by  b  will  have  a  value  \°-  b 
when  measured  by  the  scale,  and  the  dimension  denoted  by  c  will  have  a 
value  Y  c'  Tne  product  of  -1/-  a,  -1/  &,  and  Y-  ci  tliat  is>  -V°209°  a&c,  will 


66  EXPERIMENTAL   PHYSICS. 

denote  the  false  volume  found  by  using  the  measurements  indicated  by 
the  faulty  scale  ;  and  d',  the  false  density,  will  be 

d'=  W  -     72*      W.  . 

-VV^oftc      Toooa6c 
The  difference  between  the  true  density  and  the  false  is 

W  W  W  W  W 

d  ~  d/  =  tib~c  ~  **  ab~c  =  ****  ^te  ~  T^«  ^  =  T^  ^  ; 

or,  in  words,  the  value  found  for  the  density  will  be  too  small  by  0.271  of 
the  true  density. 

22.  A  block,  the  density  of  which  is  to  be  determined,  is  measured 
with  a  scale  the  divisions  of  which  are  f  as  long  as  they  are  supposed  to 
be.    How  much  too  small  or  too  large  will  the  value  found  for  the  density 
be  in  consequence  of  this  error  ? 

23.  A  cube  of  wood  10cm  on  each  edge,  and  of  sp.  gr.  0.5,  is  covered 
on  one  side  by  a  piece  of  metal  10cm  square  and  lcm  thick,  of  sp.  gr.  5. 
How  deep  would  the  whole  mass  of  wood  and  metal  sink  in  water  ? 

Solution.     Volume  of  wood  =  1000CC. 

Volume  of  metal  =  100CC. 

Volume  of  metal  and  wood  —  1100CC. 

Weight  of  wood  =  0.5  X  1000  =  500s. 

Weight  of  metal  =  5  X  100  =  500&. 

Weight  of  metal  and  wood  =  1000s. 

Since  the  volume  of  the  wood  and  the  metal  together  is  1100CC,  and 
their  weight  only  1000s,  the  composite  block  will  float  with  1000CC  of  its 
volume  beneath  the  water.  (Why  ?) 

The  composite  block  would  naturally  float  with  the  metallic  plate 
downward ;  hence,  the  outer  face  of  the  metallic  plate  would  be  10cm 
below  the  surface  of  the  water. 

24.  A  cylinder  20cm  long  consists  of  a  cylinder  of  iron,  sp.  gr.  7,  lcm 
long,  and  one  of  wood,  sp.  gr.  0.5,  19cm  long.     If  this  cylinder  floats  up- 
right in  water,  how  many  centimeters  of  its  length  will  be  above  the 
water  ? 

25.  A  cube  of  wood,  10cm  on  an  edge,  floats  in  water  with  8.5cm  of  its 
depth  submerged.     How  many  cubic  centimeters  of  its  volume  will  be 
under  water  after  kerosene,  of  sp.  gr.  0.8,  is  poured  into  the  vessel  con- 
taining the  water  till  the  block  is  completely  submerged  ? 


EXAMPLES.  67 

26.  A  piece  of  wood,  of  volume  1200CC,  floats  with  two-thirds  of  its 
volume  beneath  the  surface  of  the  water.     What  is  the  least  number  of 
cubic  centimeters  of  lead,  of  sp.  gr.  11.3,  that  must  be  attached  to  the 
block  to  submerge  it  completely  ? 

27.  A  long  tube  closed  at  one  end  is  partly  filled  with  mercury,  and 
the  remainder  with  air.     When  this  tube  is  inverted  in  a  deep  cup  of 
mercury  and  pushed  down  till  there  is  only  50cm  of  its  length  projecting 
above  the  surface  of  the  mercury  in  the  cup,  the  level  of  the  mercury  in 
the  tube  and  in  the  cup  is  the  same.     When  the  tube  is  raised  till  100cm 
of  its  length  projects  above  the  level  of  the  mercury  in  the  cup,  the  surface 
of  the  mercury  in  the  tube  stands  25cm  above  the  level  of  the  mercury  in 
the  cup.     What  is  the  pressure  of  the  atmosphere  ? 

28.  A  barometer  which  has  air  in  the  space  above  the  column  reads 
65cm.     If  the  distance  from  the  level  of  the  mercury  in  the  cistern  to  the 
top  of  the  barometer  tube  is  85cm,  and  if  the  air  in  the  tube  has  a  volume 
of  lcc  when  the  pressure  is  77cm,  find  the  true  barometric  height,  the  area 
of  the  cross-section  of  the  tube  being  l^qcm. 


CHAPTER    II. 

HEAT. 

3O.  Some  Effects  of  Heat.  •  We  shall  begin  the  study 
of  heat  with  some  experiments  for  the  purpose  of  finding 
out  whether  heat  will  change  the  size  of  bodies. 

Experiment  3O.  To  find  whether  heat  will  chayige  the 
size  of  a  volume  of  water. 

Apparatus.  A  bottle  having  a  wide  mouth,  like  the  one  used  in 
Exp.  11  ;  a  good  cork  stopple  to  fit  the  bottle ;  a  piece  of  glass  tube 
30cm  or  4ocm  long,  and  0.3cm  or  0.4cm  in  diameter  ;  a  Bunsen  burner  ; 
a  copper  boiler ;  two  little  rubber  bands ;  a  jar  of  cold  water. 

Directions.  Under  the  boiler  half  full  of  water 
place  the  lighted  Bunsen  burner.  While  the  water 
is  getting  warm,  pierce  a  hole  through  the  stopple 
with  a  cork  borer  a  little  smaller  than  the  tube. 
Push  the  tube  through  the  cork.  -  Fill  the  bottle 
brimful  of  water,  and,  taking  care  not  to  enclose  air- 
bubbles,  press  the  stopple  into  the  mouth  of  the 
bottle.  If  the  water  fills  the  tube  completely,  shake 
out  some,  so  that  the  water  will  fill  less  than  half 
the  tube.  Around  the  tube  (Fig.  26),  at  the  top  of 
the  water  column,  slip  a  rubber  band  for  a  marker. 
Have  the  water  in  the  boiler  so  hot  as  to  be  uncom- 
fortable to  the  finger  held  in  it  for  an  instant;  if 
too  hot,  add  cold  water.  Put  the  bottle  into  the 
FIG.  ?6.  n°t  water,  and  for  two  or  three  minutes  watch  the 


HEAT.  69 

column  of  water  in  the  tube.  At  the  end  of  the  two  or 
three  minutes,  put  the  other  rubber  band  on  the  tube,  at 
the  top  of  the  water  column. 

What  have  you  observed  while  you  have  watched  ? 

What  is  meant  by  expansion  ? 

When  heated,  does  the  water  in  the  bottle  expand? 

Put  the  bottle  into  the  jar  of  cold  water,  and  for  three 
or  four  minutes  watch  the  water  column. 

What  do  you  observe  ? 

What  is  meant  by  contraction  ? 

When  cooled,  does  the  water  in  the  bottle  contract? 

NOTE.  This  bottle  of  water  with  the  tube  might  be  used  to  tell  us 
which  of  two  liquids  is  the  warmer  ;  for  we  might  put  the  bottle  first 
into  one  liquid  and  then  into  the  other,  and  in  each  case  observe  the 
height  of  the  water  column  in  the  tube.  The  water  column  would  stand 
higher  for  the  warmer  liquid.  The  comparison  could  be  more  accurately 
made  by  means  of  a  peculiar  instrument,  the  thermometer  (from  two 
Greek  words  tJierme,  warmth;  and  metron,  a  measure),  which  in  action, 
and  somewhat  remotely  in  form,  resembles  our  bottle  and  tube. 

Experiment  31.  To  find  whether  water,  alcohol,  and 
ether,  when  equally  heated,  expand  equally. 

Apparatus.  Three  bulb-tubes,  with  two  little  narrow  rubber  bands 
on  each  stem  as  markers  ;  water,  alcohol,  ether  ;  a  copper  boiler. 

.  NOTE.  The  teacher  should  fill  one  bulb  and  a  part  of  its  stem  with 
water,  one  with  alcohol  and  one  with  ether,  and  should  clamp  the  bulb- 
tubes  in  a  group,  as  shown  in  Fig.  27,  to  a  retort-stand  which  is  firmly 
fastened  to  a  table.  There  should  be  no  flame  near  this  apparatus, 
as  the  vapor  of  ether  is  inflammable,  and,  with  air,  forms  an  explosive 
mixture. 

Directions.  Have  the  copper  boiler  three-quarters  full 
of  water  a  little  warmer  than  the  air  of  the  room.  On 


70 


EXPERIMENTAL   PHYSICS. 


each  tube,  which  should  have  a  label  as  in  Fig.  27,  adjust 
a  marker  to  a  level  with  the  surface  of  the  liquid  within. 

Place  the  boiler  so  that  the 
bulbs  shall  be  beneath  the 
surface  of  the  water.  Move 
neither  the  retort-stand  nor  the 
bulbs.  Watch  the  columns 
for  two  or  three  minutes. 

Make  a  table,  by  putting 
down  the  names  of  the  three 
liquids,  showing  the  relative 
expansion. 

Experiment  32.      To  find 
whether    heat   will    make    air 
FIG.  27.  expand. 

Apparatus.     The  bottle,  stopple,  and  tube  of  Exp.  30  ;    a  jar  of 
water. 

Directions.       Put    the 

stopple,  through  which 
the  tube  has  been  thrust, 
tightly  into  the  mouth  of 
the  bottle,  which  should 
contain  nothing  but  air. 
Clasp  the  bottle  in  the 
hand,  covering  it  more 
completely  than  is  shown 
in  Fig.  28,  and  push  the 
FIG'  28<  end  of  the  tube  about  lcin 

below  the  surface  of  the  water  in  the   jar.     For  one  or 
two  minutes  watch  the  water  at  the  end  of  the  tube. 


MERCURY    THERMOMETER.  71 

What  happens  in  the  water  at  the  end  of  the  tube  ? 

How  do  you  account  for  what  takes  place  ? 

Without  removing  the  end  of  the  tube  from  the  water, 
take  the  hand  from  the  bottle.  For  one  or  two  minutes 
watch  the  water  in  the  end  of  the  tube. 

What  does  the  water  in  the  end  of  the  tube  do  ? 

How  do  you  explain  this  phenomenon? 

MEROTRY    THERMOMETER. 

31.  The  Thermometer.  Upon  the  table  before  you 
place  a  mercury  thermometer,  and  make  an  accurate  sketch 
of  it  in  your  note-book. 

Observe  that  the  thermometer  consists  of  three  principal 
parts : 

1.  A  spherical  or  elongated  vessel  containing  mercury. 
This  vessel,  called  the  bulb,  corresponds  to  the  bottle  of 
Exp.  30. 

2.  A  glass  tube  of  small  bore  partly  filled  with  mercury. 
This  tube,  called  the  stem,  corresponds  to  the  tube  joined 
to  the  bottle  of  Exp.  30.     The  thread  of  mercury  partly 
tilling  the  stem  is  called  the  column.     The  position  of  the 
top  of  the  column  gives  the  height  of  the  thermometer. 

3.  A  scale  made  by  scratches  on  the  stem,  or  made  of 
paper  and  enclosed  in  a  glass  tube  which  also  contains  the 
stem.     This  scale  is  divided  into  equal  parts,  and  each  one 
of  these  parts  is  called  a  degree  of  temperature. 

You  will  probably  notice  in  some  thermometers  a  little 
bulb  or  slight  enlargement  at  the  top  of  the  stem.  This 
little  bulb,  if  the  thermometer  is  overheated,  catches  the 
mercury,  which  would  otherwise  press  against  the  end  of 
the  tube  and  break  it.  Before  using  a  thermometer,  be 


72  EXPERIMENTAL    PHYSICS. 

sure  to  examine  this  place,  for,  when  the  thermometer 
happens  to  get  turned  upside  down,  a  little  mercury 
frequently  lodges  here.  If  there  should  happen  to  be 
any  mercury  in  the  little  bulb,  grasp  the  stem  at  the 
end,  where  the  little  bulb  is,  firmly  in  the  hand.  Extend- 
ing the  arm  to  its  full  length,  raise  the  hand  so  that  the 
large  bulb  shall  point  towards  the  ceiling.  Then,  carrying 
the  hand  forward,  with  a  quick  sweep,  bring  it  to  its 
natural  position  by  the  side,  thus  making  the  large  bulb 
trace  out  a  semicircle  in  the  air.  A  single  energetic  treat- 
ment is  usually  sufficient  to  dislodge  the  mercury. 

Before  using  a  thermometer,  look  carefully  also  along 
the  stem  at  the  column,  which  is  sometimes  broken,  that 
is,  separated  into  two  or  more  parts.  In  case  the  column 
is  broken,  firmly  grasp  the  stem,  with  the  bulb  downwards, 
at  its  middle  part  in  the  fingers  of  the  right  hand.  Keep- 
ing the  stem  vertical,  raise  the  hand  a  little  way,  and  then 
bring  the  hand  down  sharply  upon  the  palm  of  the  left 
hand.  In  most  cases  this  treatment  once  or  twice  repeated 
suffices  to  mend  the  column. 

On  that  part  of  the  scale  lying  to  the  right-hand  side  of 
the  stem  you  will  notice  in  many  thermometers  a  column 
of  ciphers ;  while  on  the  left-hand  side  you  will  see  a 
column  of  figures.  A  cipher  on  the  right-hand  side 
belongs  with  the  figure  opposite,  so  we  have  10,  20, 
30,  etc.  The  space  between  10  and  20,  20  and  30,  etc., 
is  divided  into  10  equal  parts,  or  degrees. 

The  thermometer  that  we  have  described  is  called  a 
chemical  thermometer  with  a  Centigrade  scale.  This  is 
the  thermometer  which  we  shall  use  in  all  our  work  in 
heat. 


MERCURY   THERMOMETER.  73 

Experiment  33.  To  find  what  temperature  a  thermom- 
eter indicates  when  placed  in  melting  ice. 

Apparatus.     A  thermometer ;  a  beaker  full  of  snow  or  broken  ice. 

Directions.  In  a  vertical  position,  in  the  beaker  of 
broken  ice,  put  the  thermometer  so  that  its  bulb  and  a 
part  of  its  stem  shall  be  covered.  Watch  the  column. 
After  a  time  the  column  ceases  to  fall  and  comes  to  rest. 
The  column  is  now  said  to  be  stationary.  By  repeatedly 
trying  this  experiment,  physicists  have  found  that  the 
temperature  of  clean  ice,  when  melting,  is  always  the  same. 

Why  does  the  column  fall  ? 

From  the  position  of  the  column,  what  symbol  should 
you  infer  is  used  to  indicate  the  temperature  of  melting 
ice? 

Experiment  34.  To  find  the  temperature  a  thermom- 
eter indicates  when  placed  in  boiling  water. 

Apparatus.  A  thermometer ;  a  beaker  ;  a  retort-stand  and  ring  ; 
a  piece  of  wire  gauze  about  15cm  square  ;  a  Bunsen  burner. 

Directions.  After  wiping  the  beaker  dry  on  the  out- 
side, set  it  half  full  of  water  on  the  wire  gauze  laid  on  the 
ring  of  the  retort-stand.  Place  the  lighted  Bunsen  burner 
beneath  to  heat  the  water.  Dip  the  thermometer  bulb  into 
the  water,  and  watch  the  column  until  the  water  boils. 

Does  the  column  become  stationary  soon  after  the  water 
begins  to  boil  ? 

NOTE.  Physicists  have  found  that  the  temperature  of  boiling  water, 
or,  more  accurately,  the  temperature  of  the  steam  from  boiling  water,  is 
constant  only  when  certain  conditions  are  fulfilled.  These  conditions  we 
shall  soon  consider. 


74  EXPERIMENTAL    PHYSICS. 

32.  The  Fixed  Points.     By  Exps.  33  and  34  you  have 
become  acquainted  with  two  remarkable  points  of  the  ther- 
mometer scale,  the  melting-point  of  ice,  commonly  called 
the  freezing-point ;   and  the  boiling-point  of  water.     These 
two  points  are  called  fixed  points,  as  each  of  them,  under 
proper  conditions,  represents  an  invariable  temperature. 

On  the  Centigrade  scale,  the  space  between  the  fixed 
points  is  divided  into  100  degrees.  Divisions  are  often 
carried  along  the  scale  below  the  freezing-point  and  above 
the  boiling-point.  Divisions  below  the  point  marked  zero 
(0)  are  indicated  by  the  negative  sign;  thus,  — 10°  ^C. 
means  10  degrees  below  the  freezing-point  (0)  on  the  Cen- 
tigrade scale.  The  mark  °  stands  for  degree  or  degrees. 

33.  Heat    and    Temperature.      The   terms    heat  and 
temperature  are  used  in  physics  so  frequently  and  are  of 
such  importance  that  particular  attention  will  be  given  to 
the  meaning  of  these  terms  in  the  following  experiment. 

Experiment  35.  To  find  whether  heat  and  temperature 
are  the  same. 

Apparatus.  A  Bunsen  burner  ;  a  retort-stand  and  ring  ;  a  piece  of 
wire  gauze  about  15cm  square  ;  two  beakers  of  equal  size  ;  a  ther- 
mometer. 

Directions.  Fill  one  of  the  beakers  one-third  full  of 
cold  water,  the  other  two-thirds  full.  Place  them  side  by 
side  on  the  gauze  laid  on  the  ring  of  the  retort-stand. 
Put  the  Bunsen  burner  beneath,  in  a  position  to  heat 
both  beakers  equally. 

When  the  water  begins  to  boil  in  one  of  the  beakers, 
find  its  temperature  with  the  thermometer,  and  immedi- 


TEMPERATURE    AND    PRESSURE.  75 

ately  afterward  get  the  temperature  of  the  water  in  the 
other  beaker. 

Is  the  temperature  higher  in  one  beaker  than  in  the  other  ? 

If  the  same  quantity  of  heat  had  entered  each  beaker, 
what  inference  can  you  draw  ? 

Does  a  thermometer  indicate  the  quantity  of  heat  a 
body  contains  ? 

Definition.  Heat  is  that  which  is  capable  of  producing 
in  us  the  sensation  of  warmth. 

Definition.  The  temperature  of  a  body  tells  us  the 
intensity  of  the  heat  in  it. 

TEMPERATURE   AND    PRESSURE. 

34.  The  Relation  between  the  Temperature  at 
which  Water  boils  and  the  Amount  of  Atmospheric 
Pressure.  On  high  mountains,  like  those  in  Colorado, 
one  must  boil  an  egg  for  five  minutes  in  order  to  cook  it 
as  hard  as  if  it  had  been  boiled  for  three  minutes  at  the 
seashore.  If  we  really  knew  that  water  when  boiling  on 
a  mountain  has  a  lower  temperature  than  when  boiling  at 
the  seashore,  this  fact  could  be  easily  explained. 

As  it  is  not  convenient  for  us  to  climb  a  mountain,  boil 
water  on  the  mountain  side,  and  test  the  temperature  of 
this  boiling  water  with  a  thermometer,  we  shall  bring 
about  in  the  laboratory  conditions  similar  to  those  at 
the  top  of  a  mountain.  The  pressure  of  the  air  on 
a  mountain  is  less  than  the  pressure  at  the  foot  of  the 
mountain,  so  in  the  next  experiment  we  shall  get  the  tem- 
perature of  water  when  it  is  boiling  under  a  reduced 
pressure. 


76  EXPEBIMENTAL  PHYSICS. 

Experiment  36.  To  find  what  influence  a  diminution 
of  pressure  has  upon  the  boiling-point  of  water. 

Apparatus.  A  250CC  Kjeldahl  flask  ;  a  rubber  stopple  with  two 
holes  to  fit  the  flask ;  a  thermometer  ;  a  piece  of  glass  tube  about 
15cm  long,  bent  at  right  angles,  and  of  a  size  to  fit  one  of  the  holes  in 
the  stopple ;  a  piece  of  pressure  tube  about  10cm  long  ;  a  Bunsen 
burner  ;  an  air-pump  ;  a  piece  of  pressure  tube  about  40 cm  long,  with 
a  pointed  glass  tube  in  one  end ;  a  retort-stand  with  two  rings. 

Directions.  Place  the  retort-stand  beside  the  air-pump, 
and  over  the  exhaust  nozzle  slip  the  end  of  the  pressure 
tube.  Have  the  flask  half  full  of  water.  Through  one 
hole  of  the  stopple  push  the  bent  tube ;  through  the  other, 
the  thermometer,  so  that  its  bulb  will  be  2cm  or  3cm  from 
the  bottom  of  the  flask  when  the  stopple  is  in  place. 
Insert  the  stopple,  and  over  .the  end  of  the  glass  tube 
slip  the  rubber  tube.  See  that  there  is  a  free  exit  through 
the  tube  from  the  inside  of  the  flask  to  the  open  air,  lest 
there  should  be  a  dangerous  explosion  on  heating  the  flask. 

Hold  the  flask  by  the  extremity  of  its  neck,  and,  avoid- 
ing an  exposure  to  the  flame  of  any  part  of  the  vessel  not 
covered  by  water,  heat  gradually.  When  the  water  boils, 
note  the  temperature  indicated  by  the  thermometer.  In 
case  the  neck  becomes  clouded  with  mist,  making  it  impos- 
sible to  read  the  thermometer,  throw  a  dry  cloth  or  towel 
around  the  flask,  and,  by  tipping  it,  cause  a  little  water  to 
run  into  the  neck  to  wash  away  the  mist.  Take  the  flask 
to  the  air-pump,  and  support  it,  as  shown  in  Fig.  29,  by 
the  rings  of  the  retort-stand.  By  inserting  into  the  piece 
of  pressure  tube  on  the  flask  the  pointed  bit  of  glass  tube 
attached  by  the  long  rubber  tube  to  the  air-pump,  connect 
the  flask  and  the  air-pump. 


TEMPERATURE    AND   PRESSURE.  77 

Before  you  begin  to  pump,  record  the  temperature  of 
the  water. 

Is  the  water  boiling,  that  is,  are  bubbles  rising  through 
the  mass  of  the  water  and  breaking  at  the  surface  ? 

Make  one  or  two  strokes  of  the  pump. 

What  happens  in  the  flask? 

After  two  or  three  minutes  make  one  or  two  strokes 
more  of  the  air-pump. 

What  happens  in  the  flask  ? 

Record  the  temperature  the  water  now  has. 

From  the  facts  obtained 
in  this  experiment,  what 
inference  can  you  draw? 

Why  does  it  take  a 
longer  time  to  cook  an 
egg  on  a  mountain  than 
at  the  sea-level  ? 

Experiment     37.       To 

find  what  influence  an  in- 
crease of  pressure  has  upon 
the  boiling-point  of  water.  FK!  29' 

Apparatus.  With  the  exception  of  the  air-pump,  the  same  as  in 
the  last  experiment ;  also,  a  retort-stand  with  two  rings  ;  a  piece  of 
wire  gauze  15cm  square  ;  a  glass  tube  bent  at  right  angles',  with  one 
arm  about  30cm  long  and  the  other  about  5cm ;  an  iron  pan  ;  a  test- 
tube  ;  mercury  ;  a  cloth  ;  blotting-paper. 

Directions.  Put  the  flask  half  full  of  water  upon  the 
wire  gauze  laid  on  one  of  the  rings  of  the  retort-stand. 
Over  the  neck  of  the  flask  pass  the  other  ring,  and  clamp 
it  to  the  retort-stand  to  keep  the  apparatus  from  tipping 


78 


EXPERIMENTAL    PHYSICS. 


over.  Slip  the  short  arm  of  the  tube  into  the  bit  of  pres- 
sure tube  attached  to  the  stopple.  Put  the  stopple  into 
the  flask,  and  heat  the  water  to  boiling.  Record  the  tem- 
perature of  the  boiling  water.  If  necessary,  wash  away 
the  mist  as  in  the  last  experiment. 

Pour  mercury  into  the  test-tube  to  the  depth  of  about 
3cm.  When  the  steam  is  coming  freely  from  the  end  of 
the  glass  tube,  wrap  a  cloth  round  the  test-tube,  and,  hold- 
ing it  over  the  pan,  not  shown  in  Fig.  30,  push  the  end 

of  the  glass  tube  to  the 
bottom  of  the  test-tube. 

Have  you  increased  the 
pressure  in  the  flask  ? 

Watch  the  thermome- 
ter. 

What  is  now  the  tem- 
perature of  the  boiling 
water  ? 

As  soon  as  the  mercury 
begins    to    sputter,    take 
the  test-tube    away,  and 
remove     the     water    on 
the    mercury    with    blotting-paper. 

From  the  facts  obtained  by  this  experiment,  what  infer- 
ence can*  you  draw  ? 

35.  Boiling-Point  of  Water.  Men  of  science  through- 
out the  world  have  agreed  to  denote  by  100°  Centigrade 
the  temperature  which  a  thermometer  indicates  when 
placed  in  steam  from  water,  which  is  boiling  in  an  open 
vessel  when  the  atmospheric  pressure  is  760mm  (that  is, 


FIG.  so. 


DETERMINATION    OF    FIXED    POINTS.  79 

when  the  atmospheric  pressure  is  sufficient  to  support  a 
column  of  mercury  760mm  high).     Hence,  the 

Definition.  Water  boils  at  100°  (7.,  when  the  atmos- 
pheric pressure  is  760mm. 

Careful  experiments  have  shown  that  the  temperature 
of  water,  boiling  when  the  pressure  differs  but  little  from 
760mm,  may  be  found  by  adding  1°  for  each  27mm  of  pres- 
sure above  760nun,  or  by  subtracting  1°  for  each"  27mm  of 
pressure  below  760mm.  Examples  like  those  which  follow 
may  make  this  clearer. 

EXAMPLES. 

1.  When  the  pressure  of  the  atmosphere  is  742mm,  the  reading,  in 
steam,  of  a  thermometer  whose  scale  was  not  properly  adjusted  by  the 
maker  is  98°.  5.      What  would  be  the  reading  of  the  instrument  for  a 
pressure  of  700mm  ? 

Solution.  760  —  742  =  18mm.  As  27mm  make  a  difference  of  1°,  18mm 
would  make  a  difference  of  |-f  of  1°,  that  is,  0°.67.  Hence,  the  reading  of 
the  thermometer,  when  the  pressure  is  760mm,  would  be  98°.  5  +  0°.67  = 
99°.  17. 

2.  In  the  example  just  given,  if  the  pressure  had  been  778mm  and  the 
thermometer  reading  100°.  4,  what  would  have  been  the  reading  for  a 
pressure  of  760ml»  ? 

DETERMINATION    OF   FIXED    POINTS. 

36.  Errors  of  Thermometer  Scale.  After  the  mer- 
cury has  been  put  into  the  bulb,  and  the  stem  sealed, 
the  next  step  in  making  a  thermometer  is  to  adjust  the 
scale.  In  order  to  adjust  the  scale,  it  is  necessary  to 
determine  the  two  fixed  points.  One  of  the  fixed  points 
is  determined  by  putting  the  bulb  and  a  part  of  the 


80  EXPERIMENTAL    PHYSICS. 

stem  into  melting  ice.  By  putting  the  thermometer  into 
steam  coming  from  boiling  water,  the  other  fixed  point  is 
found  and  marked,  as  was  the  first  one,  upon  the  stem. 
We  have  already  learned  that  on  the  Centigrade  scale  the 
freezing-point  is  marked  0,  and  the  boiling-point  100,  and 
also  that  the  space  between  the  two  points  is  divided  into 
100  equal  parts. 

In  adjusting  the  scale,  the  maker  of  a  cheap  thermom- 
eter does  not  use  care ;  hence,  frequently,  the  thermom- 
eter does  not  indicate  the  true  temperature.  So  careful 
is  a  physicist  to  have  his  thermometer,  though  made 
by  a  skilled  workman,  accurate  for  delicate  work,  that  he 
always  tests  the  scale  for  himself.  He  finds  the  errors  of 
the  thermometer,  and  in  his  work  makes  allowances  for 
them. 

Of  the  two  common  errors  of  a  thermometer,  one  arises 
in  marking  the  position  of  the  freezing-point ;  the  other, 
in  marking  the  position  of  the  boiling-point. 

To  test  a  thermometer  for  the  accuracy  of  its  freezing- 
point  and  the  accuracy  of  its  boiling-point  will  be  the  object 
of  the  next  experiment. 

Experiment  38.  To  find  ivhether  the  fixed  points  of  a 
thermometer  have  been  properly  marked  on  the  scale. 

(For  convenience  we  shall  divide  this  experiment  into  three  parts.) 
PART  1.  To  find  the  position  of  the  freezing-point. 
Apparatus.  A  thermometer  ;  finely  broken  ice  ;  a  beaker. 

Directions.  Fill  the  beaker  with  clean,  finely  broken 
ice.  Add  enough  water  to  fill  the  spaces  between  the 
lumps  of  ice.  Push  the  bulb  of  the  thermometer  vertically 


DETERMINATION    OF   FIXED   POINTS.  81 

into  the  middle  of  the  beaker  with  its  stem  vertical  until 
the  point  marked  0°  is  only  lmm  or  2mm  above  the  surface 
of  the  ice,  which  should  be  heaped  up  in  the  beaker. 
When  the  column  ceases  to  fall,  record  the  reading.  In 
this  experiment,  as  well  as  in  other  heat  experiments,  read 
the  thermometer  with  care.  Try  to  read  to  tenths  of  a 
degree.  In  reading,  be  careful  to  place  the  eye  in  such 
a  position  that  a  straight  line  drawn  from  the  center  of  the 
eye  would  strike  the  thermometer  at 
right  angles  at  the  top  of  the  column. 

PART  2.    To  find  the  position  of  the 
boiling-point. 

Apparatus.     The  thermometer  of  Part  1  ; 
a  copper  boiler  with  a  copper  cone. 

Directions.  Fill  the  copper  boiler 
with  water  to  a  depth  of  3cm  or  4cm. 
Get  a  cone  that  will  fit  tightly,  and  put 
it  in  place  on  the  boiler.  Into  the  side 
tube  leading  from  the  boiler  put  a  cork. 
Do  not  stop  up  the  side  tube  leading 
from  the  cone.  (Why?)  Get  a  cork 
stopple  that  will  fit  the  hole  in  the  top 
of  the  cone.  In  this  stopple,  with  a 
cork  borer,  make  a  hole  through  which 
to  pass  the  thermometer.  Put  the 
stopple  in  place  in  the  top  of  the  cone, 
and  through  the  stopple  carefully  push 
the  thermometer  (Fig.  31)  until  the 
point  marked  100°  is  not  more  than  2mm  or  3mm  above  the 
top  of  the  stopple.  The  bulb,  however,  must  not  come 


82  EXPERIMENTAL   PHYSICS. 

within  less  than  2cm  or  3cm  of  the  water  in  the  boiler. 
Using  only  one  Bunsen  burner,  keep  the  water  boiling 
till  the  mercury  column  stops  rising ;  then  record  its 
position. 

We  have  heated  the  bulb  and  a  large  part  of  the  stem 
in  the  steam.  Now  draw  up  the  thermometer  till  the 
point  marked  0°  is  just  above  the  stopple.  Record  the 
point  at  which  the  column  becomes  stationary. 

If  this  point  is  different  from  the  one  you  found  when 
the  bulb  and  a  large  part  of  the  stem  were  in  the  steam, 
how  do  you  account  for  the  difference  ? 

SUGGESTION.  Consider  whether  in  both  cases  all  the  mercury  has 
been  heated  to  the  same  temperature. 

At  the  time  of  performing  the  experiment,  record  the 
reading  of  the  barometer. 

Why  is  it  necessary  to  know  the  reading  of  the  barom- 
eter? (See  Exps.  36  and  37.) 

If  the  atmospheric  pressure  had  been  760mm  when  the 
bulb  and  the  stem  were  in  the  steam,  find  by  computation 
where  the  boiling-point  (100°)  would  have  come  on  the 
scale  of  your  thermometer.  (See  Ex.  at  end  of  Art.  35.) 

We  have  already  done  all  the  .work  necessary  to  find 
simply  whether  the  freezing-point  and  the  boiling-point 
have  been  correctly  marked  on  the  scale  of  the  thermom- 
eter. Part  3  of  the  experiment  is  to  bring  out  another 
peculiarity  of  thermometers. 

PART  3.  To  find  the  position  of  the  freezing-point 
again. 

Apparatus.  The  same  as  in  Part  1,  with  a  fresh  supply  of  broken 
ice. 


DETERMINATION    OF    FIXED    POINTS.  83 

Directions.  If  the  thermometer  has  just  been  taken 
from  the  steam,  let  the  thermometer  remain  in  the  air  till 
the  column  has  fallen  to  a  height  of  about  40°  or  50°. 
(Why?)  Fill  the  beaker  again  with  clean,  finely  broken 
ice,  and  repeat  Part  1.  After  the  column  ceases  to  fall, 
record  its  position. 

Is  the  column  of  mercury  shorter  or  taller  than  that  of 
Part  1,  and  how  much? 

37.  Elevation  of  the  Zero-Point;  Temporary  Lower- 
ing- of  the  Zero-Point.  When  the  bulb  of  a  thermometer 
is  put  into  ice-water,  the  bulb  contracts  and  a  slight  eleva- 
tion of  the  column  is  often  observed,  followed  by  a  fall  of 
the  column  immediately,  or  as  soon  as  the  mercury  in  the 
bulb  feels  the  change  in  temperature.  Even  when  the 
thermometer  is  kept  in  a  place  of  uniform  temperature, 
careful  observers  have  noted  that  the  bulb  of  a  new  ther- 
mometer shrinks  gradually  and  perceptibly  for  some  weeks 
or  months.  This  gradual  shrinkage  of  the  bulb  raises  the 
zero-point  and  introduces  an  error  known  as  the  eleva- 
tion of  the  zero -point. 

The  cause  of  this  shrinkage  is  that  the  bulb,  which  was 
formed  by  blowing  the  glass  in  its  plastic  state,  cooled 
before  its  particles  had  time  to  regain  the  relative  posi- 
tions which  they  had  before  the  pressure  necessary  to  the 
operation  of  blowing  was  applied.  As  time  goes  on,  these 
particles,  rapidly  at  first,  but  after  a  while  more  and  more 
gradually,  begin  to  accommodate  themselves  to  one  another, 
and  thus  produce  the  shrinkage. 

On  the  other  hand,  even  in  good  thermometers,  the 
expansion  of  the  bulb,  produced  by  heating  it  to  the 


84  EXPERIMENTAL   PHYSICS. 

temperature  of  boiling  water,  lasts  for  a  little  while  and 
produces  a  temporary  lowering  of  the  zero-point. 

In  testing  a  thermometer,  why  should  the  operation  of 
finding  the  freezing-point  come  first  ? 

38.  Important  Precaution  in  Testing-  the  Boiling- 
Point  of  a  Thermometer.  When  testing  the  boiling- 
point  of  your  thermometer,  you  were  directed  not  to 
allow  the  bulb  to  dip  into  the  boiling  water ;  you  were  to 
allow  the  steam,  not  the  water,  to  come  in  contact  with 
the  bulb.  The  reasons  for  this  precaution  will  be  brought 
out  in  the  next  experiment  and  the  discussion  that  comes 
after  it. 

Experiment  39.  To  find  whether  salt  water  will  boil  at 
the  same  temperature  as  fresh  water. 

Apparatus.  Two  beakers  of  equal  size  ;  a  Bunsen  burner  ;  a 
retort-stand  and  ring  ;  a  piece  of  wire  gauze  about  15cm  square  ;  a 
thermometer  ;  a  spoonful  of  salt. 

Directions.  Fill  each  beaker  half  full  of  fresh  water. 
Into  one  put  a  spoonful  of  salt.  Set  the  beakers  side  by 
side  on  the  wire  gauze  over  the  flame.  When  the  liquids 
are  boiling,  record  the  temperature  of  each. 

When  boiling,  which  liquid  has  the  higher  temperature  ? 

In  getting  the  boiling-point  of  a  thermometer,  can  you 
give  a  reason  why  it  is  not  best  to  allow  the  bulb  to  dip 
into  the  water? 

NOTE.  Besides  the  possibility  of  impurities  in  the  water,  there  is 
another  reason  that  forbids  us  to  let  the  thermometer  dip  into  the  water. 
Gay-Lussac  found  that,  for  a  given  atmospheric  pressure,  water  boils  at 
different  temperatures  in  different  kinds  of  vessels.  For  example,  he 
found  the  temperature  of  water  boiling  in  a  glass  vessel  to  be  higher  than 


EXPANSION    OF    A    SOLID.  85 

that  of  water  boiling  at  the  same  time  in  a  metallic  vessel.  It  was  shown, 
however,  by  Rudberg  that  the  temperature  of  the  steam  which  escapes 
from  boiling  water  is  the  same  in  any  kind  of  vessel,  and  depends  only 
on  the  pressure  at  the  surface  of  the  water.  As  the  result  of  a  large 
number  of  experiments,  Rudberg  showed  that  the  temperature  of  steam 
coming  from  impure  water  was  the  same  as  that  of  steam  coming  from 
pure  water. 

EXPANSION    OF    A    SOLID. 

39.    Cubical    Expansion ;     Linear     Expansion.       By 

Exp.  30  we  learned  that  water  (a  liquid)  expands  when 
heated,  and  by  Exp.  32  that  air  (a  mixture  of  two  gases) 
also  expands  when  heated.  When  a  substance  (as  the 
water  in  the  bottle  of  Exp.  30)  expands  in  all  directions, 
\ve  have  what  is  called  cubical  expansion.  In  general,  all 
of  the  solid  substances  that  have  been  examined  expand 
in  all  directions  as  the  temperature  rises.  Often,  how- 
ever, the  expansion  in  length  only  is  observed  or  measured. 
This  increase  in  the  length  is  called  the  linear  expansion  of 
the  solid.  No  two  metals  expand  the  same  amount  for  the 
same  rise  of  temperature. 

The  following  is  an  experiment  on  the  measurement  of 
the  linear  expansion  of  a  solid. 

Experiment  4O.  To  find  by  what  part  of  its  original 
length  a  rod  of  brass  increases  when  its  temperature  is 
raised  1°. 

Apparatus.  A  Bunsen  burner  ;  the  copper  boiler  with  cone  (a 
sterilizing  can  makes  an  excellent  steam  generator  in  place  of  the 
boiler  and  cone);  two  pieces  of  rubber  tube,  one  about  60cm  long, 
the  other  about  10cm  ;  dividers;  a  thermometer;  a  meter  stick; 
linear  expansion  apparatus.  The  linear  expansion  apparatus  consists 
of  a  cylindrical  tube,  called  the  jacket,  which  is  made  of  galvanized 


86 


EXPERIMENTAL   PHYSICS. 


iron  and  is  closed  at  each  end  with  a  cork.  Through  a  hole  in  each 
cork  runs  a  brass  tube  whose  expansion  is  to  be  measured.  Pointing 
at  right  angles  to  its  length,  the  jacket  has  two  small  side  tubes,  one 
near  each  end  and  another  in  the  middle.  The  jacket  is  set  in  a 
horizontal  position  upon  a  wooden  frame.  On  the  frame  is  a  vertical 
scale  and  a  pointer.  The  pointer  can  be  moved  along  the  scale  by 
the  expanding  rod. 

Directions.  Lay  the  jacket  (Fig.  32)  in  its  place  upon 
the  frame.  Rest  one  end  of  the  brass  tube  against  the 
screw,  at  the  end  of  the  frame  remote  from  the  scale. 


FIG.  32. 

The  bit  of  steel  wire  soldered  to  the  other  end  of  the  brass 
tube  should  press  against  the  hinge  of  the  pointer.  Into 
the  short  tube  at  the  middle  of  the  jacket  fit  a  perforated 
cork  through  which  the  thermometer  passes.  Over  the 
end  of  the  little  side  tube  of  the  jacket  next  the  pointer 
slip  an  end  of  the  long  rubber  tube ;  also  slip  an  end  of  the 


EXPANSION    OF    A    SOLID.  87 

short  rubber  tube  over  the  end  of  the  side  tube  at  the 
other  end  of  the  jacket.  Place  a  beaker  under  the  end  of 
this  tube  in  order  to  catch  the  condensed  steam  that  would 
otherwise  drip  upon  the  table.  To  prevent  the  jacket  from 
rotating,  make  the  side  tube,  having  the  long  rubber  tube 
attached,  rest  against  the  post  that  supports  the  pointer. 
Measure  in  centimeters  and  fractions  of  a  centimeter  the 
long  arm  of  the  pointer,  that  is,  from  the  center  of  the 
hinge  screw  (the  screw  by  which  the  pointer  is  pivoted) 
to  the  side  of  the  scale  facing  the  cylinder.  With  a  pair 
of  dividers  get  in  centimeters  and  fractions  of  a  centimeter 
the  length  of  the  short  arm  of  the  pointer,  that  is,  from  the 
center  of  the  hinge  screw  to  a  point  on  a  level  with 
that  where  the  bit  of  steel  wire  touches  the  hinge. 
See  that  the  end  of  the  brass  rod  is  resting  against  the 
screw  at  the  end  of  the  frame ;  if  it  is  not,  press  it  back 
till  it  touches  the  screw.  Take  the  reading  of  the  ther- 
mometer and  also  the  reading  of  the  pointer  on  the  scale. 
In  taking  the  reading  on  the  scale,  place  the  eye  in  such 
a  position  that  the  line  of  vision  just  grazes  the  upper 
surface  of  the  pointer. 

Have  the  boiler  one-third  full  of  water.  Put  the  cone 
in  place  and  close  its  top  by  a  stopple,  also  its  side  tube. 
Do  not  disturb  the  frame,  pointer,  or  jacket.  By  means  of 
the  long  rubber  tube  already  attached,  join  the  jacket  to 
the  boiler.  Heat  the  water  in  the  boiler  and  let  the  steam 
flow  through  the  jacket  until  the  thermometer  column 
becomes  stationary.  Record  the  reading  of  the  thermom- 
eter and  also  the  new  reading  of  the  pointer.  By  laying 
the  meter  stick  beside  the  jacket,  get  the  length  in  centi- 
meters of  the  brass  rod  in  the  jacket  from  the  outside 


88  EXPERIMENTAL   PHYSICS. 

of  one  stopple  to  the  outside  of  the  other.  This  meas- 
urement is,  of  course,  a  very  rough  one,  and  may  be 
taken  at  any  stage  of  the  experiment. 

From  the  measurements  you  have  made  in  this  experi- 
ment answer  the  following  questions : 

(1)  What  is  the  distance  in  centimeters  that  the  pointer 
moves  over  in  going  from  its  lowest  position  to  its  highest 
on  the  scale  ? 

(2)  How  many  times  does  the  movement  of  the  pointer 
multiply  the  elongation  of  the  brass  rod? 

SUGGESTION.  Divide  the  length  of  the  long  arm  by  that  of  the  short 
one. 

(3)  What  is  the  amount  computed  (from  (1)  and  (2))  of 
the  elongation  of  the  brass  in  centimeters  ? 

(4)  Through  how  many  degrees  of  temperature  was  the 
brass  raised? 

(5)  What  is  the  average  amount  of  elongation  of  the 
brass  for  1°? 

(6)  What  is  the  length  of  the  brass  rod  in  centimeters 
from  the  outside  of  one  stopple  to  the  outside  of  the  other  ? 

(7)  By  what  part  of  its  original  length  (the  length  given 
in  the  answer  to  (6))  has  the  brass  rod  increased  for  an 
increase  in  temperature  of  1°  ? 

The  answer  to  (7)  is  called  the  coefficient  of  linear  expan- 
sion of  brass,  hence  the 

Definition.  The  coefficient  of  linear  expansion  tells  by 
what  part  of  its  length  a  body  has  increased  for  a  rise  in 
temperature  of  1°. 

Is  the  coefficient  of  linear  expansion  a  quantity  or  a 
number  ? 


EXPANSION    OF    A    SOLID.  89 


EXAMPLES. 

1.  A  rod  of  brass  at  15°  measures  2  ft.  in  length  ;  at  95°  it  measures 
2.003  ft.     Find  the  coefficient  of  linear  expansion. 

Solution.        Increase  in  length  of  rod  =  2.003  —  2    =  0.003  ft. 
Increase  in  temperature   =       95  —  15  —  80°. 

Increase  in  length  of  rod  for  a  rise  in  temperature  of  1°  is 
0.003  ^  80  =  0.0000375. 

The  coefficient  of  linear  expansion  =  0.0000375  -r  2  =  .000019. 

The  reason  for  calling  this  number  a  coefficient  comes  from  the  fact 
that  the  amount  a  given  length  of  brass  will  expand,  when  its  temper- 
ature is  raised  1°,  can  be  found  by  multiplying  the  given  length  by 
0.000019,  that  is,  we  use  it  just  as  in  algebra,  where  a  coefficient  is  a 
numerical  value  multiplied  into  a  quantity. 

2.  A  bar  of  lead  whose  length  at  0°  was  152.32cm  was  heated  to  100°, 
when  its  length  was  found  to  be  152.76cm.     Find  the  coefficient  of  linear 
expansion  of  lead. 

3.  A  copper  rod  that  was  15m  long  at  0°  was  found  to  have  increased 
in  length  by  2.6cra,  owing  to  a  rise  of  100°  in  temperature.     Find  the 
coefficient  of  linear  expansion  of  copper. 

4.  The  length  of  an  iron  rail  at  15°  is  30  ft.    What  will  be  its  length  at 
10°  and  at  20°  ?    The  coefficient  of  linear  expansion  of  this  iron  is  ¥T|off- 

Solution.  ¥Ti^  =  0.0000122. 

To  find  the  length  of  the  rail  at  10° :  In  cooling  1°  the  rail  would  shrink 
by  0.0000122  X  30  ft.,  or  0.000366  ft.;  but  in  cooling  5°  it  would  shrink 
by  an  amount  equal  to  5  X  0.000366  ft.,  or  0.00183  ft.  Hence  the  length 
of  the  rail  at  10°  would  be 

30  -  0.00183  =  29.99  ft. 

To  find  the  length  of  the  rail  at  20° :  In  having  its  temperature  raised 
1°,  the  rail  would  expand  by  0.0000122  X  30  ft.,  or  0.000366  ft.  ;  but 
in  having  its  temperature  raised  5°  it  would  expand  by  an  amount  equal 
to  5  X  0.000366  ft.,  or  0.00183  ft.  Hence  the  length  of  the  rail  at  20° 
would  be 

30  +  0.00183  =  30.00183  ft. 

5.  What  must  be  the  length  of  a  brass  rod  at  15°  in  order  that  at 
0°  it  may  be  exactly  2m  long,  the  coefficient  of  linear  expansion  being 
0.000019  ? 


90  EXPERIMENTAL    PHYSICS. 

6.  Assuming  that  the  maximum  temperature  of  a  30-ft.  cast-iron  rail 
exposed  to  the  sun  is  50°,  and  that  the  temperature  of  the  air  at  the  time 
of  laying  the  rail  is  10°,  what  must  be  the  minimum  distance  apart  of  the 
adjacent  ends  of  two  consecutive  rails  ?     The  coefficient  of  linear  expan- 
sion is  0.000012. 

7.  The  distance  by  rail  from  San  Francisco  to  Omaha  is  1914  miles. 
Assuming  that  the   average  variation  of  temperature   throughout  the 
year  is  50°,  what  is  the  variation  in  the  total  length  of  the  rails  ?    The 
coefficient  of  linear  expansion  is  0.000012. 


EXPANSION    OF    AIR. 

4O.  Expansion  of  Air  at  Constant  Pressure ;  Dalton's 

Law.  In  Exp.  32  you  found  that  heat  makes  air  expand. 
In  the  experiment  just  performed,  you  found  by  what  part 
of  itself  a  piece  of  brass  will  increase  in  length  for  a  rise 
in  temperature  of  1°.  In  the  next  experiment  you  are  to 
find  by  what  part  of  its  volume  a  quantity  of  air,  exposed 
to  a  constant  (or  uniform)  pressure,  will  expand  for  a  rise 
in  temperature  of  1°. 

Experiment  41.  To  find  by  what  part  of  its  volume  at 
0°  an  amount  of  air,  at  constant  pressure,  will  expand  for  a 
rise  in  temperature  of  1°. 

Apparatus.  A  250CC  flask  fitted  with  a  one-hole  rubber  stopple, 
having  a  glass  tube  3mm  or  4mm  in  diameter  thrust  through,  reaching 
nearly  to  the  bottom  of  the  flask  and  projecting  about  2cm  above  the 
stopple ;  about  25cm  of  pressure  tube  (to  fit  the  glass  tube)  and  a 
pinch-cock  to  close  the  end  of  it;  ice-water;  a  Bunsen  burner;  a 
large  glass  jar  ;  a  copper  boiler. 

Directions.  Make  sure  that  the  flask  and  all  tubes  are 
dry.  Into  the  flask  insert  the  stopple  with  glass  tube. 
Connect  the  rubber  tube  with  the  glass  tube.  Let  the 


EXPANSION    OF    AIR. 


91 


pinch-cock,  as  shown  in  Fig.  33,  be  placed  at  the  extreme 
end  of  the  rubber  tube  farthest  from  the  stopple.  (Why  ?) 
Have  ready  warm  water  in  the 
boiler.  Open  the  cock  and  plunge 
the  flask  beneath  the  water,  but 
do  not  get  any  water  into  the 
flask  or  tubes.  (Why  ?)  By  lay- 
ing a  piece  of  wood,  with  a  weight 
on  it,  across  the  boiler,  keep  the 
flask  submerged.  Bring  the  water 
to  the  boiling-point.  Boil  for 
five  minutes,  so  that  the  tem- 
perature of  the  air  in  the  flask 
may  become  100°.  Close  the 
pinch-cock  and  remove  the  flask 
from  the  hot  water.  Throw  a 
cloth  round  the  flask,  as  it  may 
collapse.  (Why?)  When  cool, 
open  the  pinch-cock  under  iced  water.  When  as  much 
water  as  possible  has  entered,  close  the  cock.  Put  the  flask 
into  the  jar  filled  with  ice-water,  in  which  there  are  many 
lumps  of  ice,  and  keep  it  submerged  five  minutes,  so  that 
the  temperature  of  the  air  in  the  flask  may  become  0°. 
Have  at  hand  a  beaker  containing  ice- water,  under  the  sur- 
face of  which  again  open  the  cock.  Make  the  level  of  the 
water  in  the  flask  and  that  of  the  water  in  the  beaker  the 
same,  and  then  close  the  cock.  Remove  the  flask  from 
the  ice-water.  Loosen  the  stopple,  raise  the  rubber  tube  into 
a  vertical  position,  and  open  the  cock  to  let  the  water  run 
into  the  flask.  (Why  ?)  Get  the  volume  of  water  in  the  flask ; 
also  the  total  contents  of  the  flask  when  the  tube  is  in  place. 


FIG.  33. 


92  EXPERIMENTAL   PHYSICS. 

From  the  measurements  you  have  made  in  this  experi- 
ment answer  the  following  questions  : 

(1)  What  was  the  volume  of  air  experimented  upon  at 
100°? 

(2)  What  was  its  volume  at  0°  ? 

(3)  How  much  would  the  volume  of  air  at  0°  expand 
in  having  its  temperature  raised  100°  ? 

(4)  How  much  in  having  its  temperature  raised  1°  ? 

(5)  By  what  part  of  its  volume  at  0°  would  the  air 
expand  for  a  rise  in  temperature  of  1°  ? 

Reduce  the  decimal  fraction,  the  answer  to  (5),  to  a 
common  fraction  with  1  for  its  numerator. 

(For  example,  the  decimal  fraction  0.003  is  the  same  as  the  common 
fraction  Tff%o-  To  reduce  TT^^  to  a  fraction  having  1  for  its  numerator, 
divide  both  numerator  and  denominator  by  3.  The  result  is  3^3,  approxi- 
mately.) 

What  is  the  denominator  of  the  common  fraction  to 
which  you  have  reduced  the  decimal  fraction  ? 

At  what  temperature  would  lcc  of  air,  measured  at  0°, 
become  2CC  ? 

At  what  temperature  would  lcc  of  air,  measured  at  0°, 
become  0.5CC  ? 

The  relation  which  connects  the  different  volumes  a 
mass  of  air  may  have  and  the  corresponding  temperatures, 
and  which  enables  us  to  answer  questions  like  those  just 
asked,  is  called  Dalton's  Law. 

State  Dalton's  Law. 

NOTE.  Dalton's  Law  is  also  frequently  called  the  Law  of  Charles. 
Dalton,  in  1801,  first  published  the  law.  Gay-Lussac,  independently  of 
Dalton,  published  the  law  in  1802.  In  his  publication,  Gay-Lussac  states 
that  Charles  (1746-1823),  Professor  of  Physics  at  Paris,  had  in  1787  noted 
the  law,  but  had  never  published  it. 


EXPANSION    OF    AIR.  93 

41.    The    Air    Thermometer;     the     Absolute     Zero. 

Careful  experiments  have  shown  that  not  only  air  but  all 
gases  also  expand  by  ^-^,  or  0.00366,  of  their  volume  at 
0°  for  each  degree  in  increase  in  temperature,  and  contract 
by  a  like  amount  (of  their  volume  at  0°)  for  each  degree  in 
fall  of  temperature.  This  regularity  in  the  expansion  and 
contraction  of  gases  has  led  to  the  construction  of  the  air 
thermometer,  in  which  are  observed  the  changes  in  volume 
of  a  quantity  of  air  so  confined  that,  no  matter  how  much 
it  may  expand  or  contract,  its  pressure  will  always  be 
constant.  While  we  shall  not  describe  the  construction 
of  an  actual  air  thermometer,  an  instrument  cumbersome 
and,  in  practice,  difficult  to  use  (in  fact,  it  is  used  only 
occasionally  as  a  standard  with  which  to  compare  mercury 
thermometers  that  are  for  use  in  delicate  work),  we  shall 
describe  an  ideal  instrument  which  will  make  clear  the 
action  of  the  air  thermometer  in  practice. 

This  ideal  instrument  (Fig.  34)  consists  of  a  long  hori- 
zontal glass  tube  of  uniform  bore,  closed  at  one  end  and 
graduated  in  equal  parts.  It  contains  a  quantity  of  dry 


FIG.  34. 


air  which,  at  0°,  occupies  273  of  these  parts,  and  which  is 
cut  off  from  the  external  air  by  a  small  pellet  of  mercury. 
As  a  quantity  of  air  at  0°,  when  heated  1°,  expands  by 
2^f  of  its  volume,  it  follows  that  if  the  air  in  the  tube 
has  its  temperature  raised  1°,  the  volume  which  it  will 
occupy  will  be  274  of  these  parts.  Had  the  temperature 


94  EXPERIMENTAL   PHYSICS. 

been  raised  to  10°,  the  volume  of  the  air  would  have  been 
283  of  these  parts.  As  the  temperature  rises,  the  air  will 
occupy  more  and  more  of  these  parts.  On  the  other  hand, 
had  the  air  in  the  tube  been  cooled  to  — 1°,  the  volume 
of  air  would  have  occupied  272  parts  ;  if  cooled  to  — 10°, 
the  volume  occupied  would  have  been  263  parts.  As  the 
cooling  continues,  the  volume  of  air  goes  on  shrinking; 
and  Dalton's  Law  [The  volume  of  a  gas  measured  at  0° 
increases  (or  diminishes)  ~by  -^^  of  itself  for  every  degree 
that  the  temperature  increases  (or  diminishes).]  has  been 
found  to  hold  for  the  lowest  temperatures  that  we  have 
obtained.  So  low  a  temperature  as  — 273°  has  never 
been  reached,  but,  theoretically,  the  volume  occupied  by 
a  gas  at  this  extremely  low  temperature  would  be  no  space 
at  all.  (In  all  probability  a  gas,  when  cooled,  would 
become  a  liquid  long  before  the  temperature  fell  as  far 
as  —  273°;  should  the  gas  have  then  become  a  liquid, 
Dalton's  Law  of  course  would  no  longer  apply.) 

The  point  —  273°  is  called  the  absolute  zero  of  the 
air  thermometer,  and  it  is  extremely  convenient,  in  deal- 
ing with  questions  relating  to  gases,  to  reckon  tempera- 
tures not  from  the  freezing-point,  but  from  the  absolute 
zero.  The  closed  end  of  the  tube  is  marked  0°,  and  the 
freezing-point,  which  is  marked  0°  on  the  Centigrade 
scale,  would  be  marked  273°  on  this  absolute  scale. 
(Why?)  To  get  the  absolute  temperature  in  Centigrade 
degrees,  we  have  only  to  add  273°  to  the  reading  of  the 
Centigrade  scale. 

QUESTIONS.  What  is  the  absolute  temperature,  when  the  temperature 
on  the  Centigrade  scale  is  0°?  10°?  100°?  273°?  -10°?  -100°? 
-273°  ? 


EXPANSION    OF   AIR.  95 

Dalton's  Law  might  be  stated  thus :  The  volume  of  a 
gas  varies  directly  as  its  temperature  on  the  absolute  scale. 

EXAMPLES. 

1.  If  the  volume  of  a  certain  amount  of  gas  is  500CC  at  50°,  what  would 
be  its  volume  at  150°  ? 

Solution.     By  Dalton's  Law  in  the  form  just  stated,  we  have 

50  -I-  273  :  150  +  273  =  500  :  *, 
or  323  :  423  =  500  :  z, 

whence  323  x  =  211500, 

.-.  x  =  654.8". 

2.  A  quantity  of  oxygen  occupies  150CC  at  15°.     What  space  will  it 
occupy  if  the  temperature  is  reduced  to  0°  ? 

3.  A  gas  has  its  temperature  raised  from  8°  to  72° ;  at  the  latter  tem- 
perature it  occupies  12  liters.     What  was  its  original  volume  ? 

NOTE.     1  liter  =  1000CC. 

4.  At  0°,  the  space  occupied  by  1.293s  of  air  is  1  liter.     At  what  tem- 
perature will  the  weight  of  1  liter  of  air  be  Is  ? 

42.  Problems  involving"  both  Boyle's  Law  and 
Dalton's  Law.  When  the  pressure  changes  and  the 
temperature  does  not,  Boyle's  Law  gives  us  the  means 
of  finding  the  volume  of  a  gas;  on  the  other  hand, 
when  the  temperature  changes  and  the  pressure  does 
not,  Dalton's  Law  gives  us  the  means  of  finding  the 
volume  of  the  gas. 

There  is  a  class  of  problems  in  which  we  are  required 
to  find  the  volume  after  the  gas  has  undergone  a  change 
both  in  pressure  and  in  temperature.  In  solving  such 
problems,  first  find  the  volume  that  would  result  from  a 
change  in  pressure,  and  then  find  what  this  volume  would 
become  when  the  temperature  is  changed.  In  the  follow- 
ing set  of  examples,  both  Boyle's  Law  and  Dalton's  Law 
are  involved. 


96  EXPEEIMENTAL   PHYSICS. 


EXAMPLES. 

1.  A  gas  of  volume  304CC,  temperature  127°,  and  pressure  75cm  has  its 
pressure  raised  to  76cm  and  its  temperature  lowered  to  27°.  Find  its 
volume  after  these  changes. 

Solution.  Let  x  denote  the  required  volume,  then  collecting  what  is 
given  in  the  problem,  we  have 

V  P  t 

304  75  127 

x  76  27 

Supposing  the  temperature  to  remain  constant,  let  us  denote  by  y  the 
volume  of  the  gas  after  the  pressure  has  changed  from  75cm  to  76cm.  By 
Boyle's  Law,  we  have 

304:?y  =  76  :  75, 
76  y-  22800, 


Now  find  the  volume,  x,  which  the  volume  300CC  becomes  after  the 
temperature  has  changed  from  127°  to  27°.     By  Dalton's  Law,  we  have 

300  :  x  =  127  +  273  :  27  +  273, 
300  :  x  =  400  :  300, 
400^  =  90000, 
x  =  225CC. 

Hence,  the  volume  which  results  from  the  change  in  pressure  and  the 
change  in  temperature  is  225CC. 

2.  The  volume  of  a  certain  quantity  of  air  at  27°,  and  under  a  pres- 
sure of  75cm,  is  1000CC.     What  would  be  its  volume  at  127°  under  a  pres- 
sure of  150cm? 

3.  If  a  mass  of  air  has  a  volume  of  140CC  when  the  temperature  is 
136°.  5  and  the  pressure  is  57cm,  what  will  the  volume  become  when  the 
temperature  is  0°  and  the  pressure  is  76cm  ? 

4.  If  a  mass  of  air  has  a  volume  of  300CC  when  the  temperature  is  0° 
and  the  pressure  76cm,  what  will  the  volume  become  when  the  tempera- 
ture is  91°  and  the  pressure  is  95cm  ? 

5.  When  the  temperature  is  99°  and  the  pressure  is  95cm,  a  mass  of 
gas  has  a  volume  of  320CC.     What  must  be  the  temperature  in  order  that 
the  gas  may  have  a  volume  of  300CC,  when  the  pressure  is  76cm  ? 


TRANSMISSION    OF   HEAT.  97 

6.  If  a  mass  of  gas  has  a  volume  V\  when  the  pressure  is  PI  and  the 
temperature  is  ti ,  and  a  volume  F2  when  the  pressure  is  P2  and  the  tem- 
perature is  £2 ,  show  that 

FiPi=  F2P2 

Zi  T2 

where  TI  =  ti  +  273,     and     T2  =  tz  +  273. 


TRANSMISSION    OF    HEAT. 

43.    Conduction,  Convection,  and  Radiation  of  Heat. 

Heat  is  communicated  from  one  body  to  another  by  one  or 
more  of  the  three  ways,  conduction,  convection,  and  radia- 
tion. It  will  be  the  object  of  the  next  five  experiments  to 
make  you  acquainted  with  these  three  ways  by  which  heat 
is  communicated. 

Experiment  42.  To  find  whether  wood  or  copper  is  the 
better  conductor  of  heat. 

Apparatus.  A  match  ;  a  piece  of  copper  wire  of  the  same  size  as 
the  match  ;  a  Bunsen  burner. 

Directions.  Between  the  thumb  and  the  forefinger  of 
one  hand  hold  the  match  by  its  end ;  in  the  same  manner 
with  the  other  hand  hold  the  copper  wire.  In  the  tip  of 
the  flame  of  the  Bunsen  burner  thrust  together  the  end 
of  the  match  and  the  end  of  the  wire. 

Which  can  you  hold  the  longer  ? 

Which  is  a  good  conductor  of  heat  ? 

Which  is  a  poor  conductor  of  heat? 

Experiment  43.  To  find  ivliether  copper  or  iron  is  the 
better  conductor  of  heat. 

Apparatus.  A  Bunsen  burner  ;  a  copper  wire  and  an  iron  wire, 
each  about  10cm  long  and  as  nearly  as  possible  of  the  same  cross- 
section. 


98  EXPERIMENTAL   PHYSICS. 

Directions.  Hold  one  wire  in  each  hand  so  that  the 
ends  shall  be  together  in  the  top  of  the  flame. 

Which  is  the  better  conductor? 

What  is  the  reason  for  your  answer  ? 

Why  does  a  piece  of  oil-cloth  feel  cold  when  you  step 
upon  it  with  the  bare  feet,  while  a  piece  of  woolen  carpet 
feels  warm? 

Why  are  wooden  handles  put  on  soldering-irons  ? 

Experiment  44.  To  find  what  is  meant  by  convection  of 
heat. 

Apparatus.     A  Bunsen  burner. 

Directions.  Hold  your  open  hand  palm  downwards  as 
high  above  the  flame  of  the  Bunsen  burner  as  you  can, 
and  lower  it  gradually.  Estimate  or  measure  roughly  the 
distance  above  the  flame  at  which  the  temperature  becomes 
unbearable. 

The  gases  produced  by  the  chemical  action  in  the  flame 
are  hot  and  expand.  The  cooler  air  pushes  them  up. 
They  strike  the  hand  and  warm  it. 

Experiment  45.  To  find  whether  water  is  heated  by 
convection,  when  heat  is  applied  beneath. 

Apparatus.  A  Bunsen  burner  ;  a  retort-stand  and  ring  ;  a  piece 
of  wire  gauze  about  15cm  square  ;  a  beaker  ;  fine  sawdust  or  bran. 

Directions.  Into  the  beaker  half  full  of  water  sprinkle 
a  little  pinch  of  sawdust,  then  place  the  beaker  on  the 
gauze  and  heat  it  over  the  flame. 

By  watching  the  movements  of  the  sawdust,  should  you 
infer  that  the  water  is  heated  by  convection  ? 


TRANSMISSION   OF   HEAT.  99 

What  peculiarity  in  the  movements  of  the  sawdust 
would  lead  you  to  the  conclusion  that  the  water  in  this 
experiment  is  heated  by  convection  ? 

Experiment  46.  To  find  what  is  meant  by  radiation  of 
heat. 

Apparatus.     A  Bunsen  burner. 

Directions.  In  Exp.  44  you  found  how  close  the  hand, 
when  held  above,  could  approach  the  flame.  At  this  same 
distance  from  the  side  of  the  flame  hold  the  hand  and 
gradually  bring  it  nearer  and  nearer. 

How  close  can  the  hand  approach  ? 

Why  is  not  the  heat  which  reaches  your  hand  brought 
to  it  by  convection  ? 

Why  is  not  the  heat  conducted  to  your  hand  ? 

Heat  that  passes  through  a  medium  without  warming 
it,  but  is  capable  of  warming  an  object  even  at  a  great 
distance  from  the  source  of  heat,  is  called  radiated  heat. 

The  heat  which  we  receive  from  the  sun  reaches  our 
earth  through  the  immense  space  between  the  sun  and 
the  earth  by  radiation. 

Point  out  how  the  flame  of  the  Bunsen  burner  illus- 
trates the  three  modes  (convection,  conduction,  and 
radiation)  by  which  heat  may  pass  from  one  point  to 
another. 

By  how  many  of  the  three  modes  by  which  heat  is  trans- 
mitted is  your  school  building  warmed  ? 

In  what  way  do  the  glowing  coals  in  an  open  grate 
give  heat  to  a  room? 

Why  is  an  open  grate  a  good  means  of  ventilation  ? 


100  EXPERIMENTAL   PHYSICS. 


CALORIMETRY. 

44.    Measurements  of  Quantities  of  Heat.      In  the 

measurements  we  have  made  thus  far,  we  have  used  as 
our  unit  of  length  the  centimeter  ;  as  our  unit  of  weight, 
the  gram.  In  measuring  quantities  of  heat,  we  shall  use 
a  special  unit.  This  unit  of  heat  is  named  the  calorie 
(pronounced  cal'orie). 

Definition.  The  calorie  (the  unit  of  heat)  is  the  amount 
of  heat  required  to  raise  the  temperature  of  I9  of  water  1°. 

The  beginner  often  asks  the  question,  "  How  much  heat 
is  there  in  a  calorie  ?  "  Remember  that  the  calorie  is  a 
unit  of  heat,  just  as  the  centimeter  is  a  unit  of  length. 

Experiment  47.  To  find  whether  the  quantity  of  heat 
given  up  by  a  known  weight  of  water  in  falling  through  a 
certain  range  of  temperature  in  one  part  of  the  thermometric 
scale,  is  able  to  raise  the  same  weight  of  water  through  the 
same  number  of  degrees  in  a  different  part  of  the  scale. 

Apparatus.  Two  nickel-plated  cups  ;  a  copper  boiler  ;  a  Bunsen 
burner  ;  a  thermometer  ;  a  100CC  graduate. 

Directions.  Into  one  of  the  cups  pour  175g  of  cold 
water  (temperature  5°  to  10°),  into  the  other  pour  175g  of 
warm  water  (temperature  50°  to  60°).  Stir  the  cold  water 
with  the  thermometer  and  note  its  temperature  ;  then, 
stirring  as  before,  immediately  take  the  temperature  of 
the  warm  water.  Before  the  warm  water  has  had  time  to 
cool  below  the  temperature  you  have  noted,  pour  it  all 
into  the  cold  water,  stir  the  mixture  well  with  tKe  ther- 
mometer, and  take  the  temperature,  , 


CALOBIMETKY.  101 

Why  should  a  liquid  be  thoroughly  stirred  before  taking 
its  temperature  ? 

How  many  degrees  has  the  temperature  of  the  hot 
water  fallen? 

How  many  degrees  has  the  temperature  of  the  cold 
water  risen? 

In  what  way  (conduction,  convection,  or  radiation)  does 
the  cold  water  receive  heat  before  it  is  mixed  with  the 
warm? 

In  what  way  does  the  warm  water,  before  mixing,  lose 
heat? 

This  experiment  leads  to  the  following  definition  : 

Definition.  The  calorie  is  the  amount  of  heat  which  P 
of  water  gives  up  in  cooling  1°. 

Experiment  48.  To  find  the  temperature  resulting 
from  mixing  equal  weights  of  water  and  mercury  of  different 
temperatures. 

Apparatus.  A  copper  boiler  ;  Bnnsen  burner  ;  iron  pan  ;  ther- 
mometer ;  a  100CC  graduate  ;  three  beakers  of  nearly  equal  size  ; 
broken  ice. 

Directions.  In  the  graduate,  placed  in  the  pan,  meas- 
ure out  100g  of  mercury  (sp.  gr.  =  13.6).  Pour  the 
mercury  into  the  beaker,  and  put  the  beaker  into  the 
water  in  the  copper  boiler  with  the  lighted  burner 
beneath.  Keep  the  mercury  dry. 

Make  ready  in  a  beaker  100g  of  water  10°  colder  than 
the  air  of  the  room.  (Why?)  Have  the  mercury  10° 
warmer  than  the  air  of  the  room.  (Why?)  Then  pour 
both,  the  water  first,  into  the  third  beaker,  which  should 
have  the  same  temperature  as  the  air  of  the  room,  the 


102  EXPERIMENTAL   PHYSICS. 

temperature  that  it  will  have,  of  course,  if  the  beaker  has 
been  standing  in  the  room  for  a  little  while.  With  the 
thermometer,  stir  the  two  liquids  thoroughly,  for  about 
half  a  minute.  Note  the  temperature  of  the  mixture. 

Which  liquid  appears  to  have  had  the  greater  influence 
in  producing  the  final  temperature  ? 

Using  the  same  weights  of  water  and  dry  mercury  as 
before,  repeat  the  experiment ;  only  have  the  temperature 
of  the  mercury  10°  below  the  temperature  of  the  air  of 
the  room,  and  the  water  10°  above  the  temperature  of  the 
air  of  the  room. 

In  this  case  which  liquid  has  the  greater  effect  in  pro- 
ducing the  final  temperature  ? 

Would  it  take  as  much  heat  to  warm  lg  of  mercury  1° 
as  to  warm  lg  of  water  1°? 

45.  Thermal  Capacity;  Calorimetry ;  Method  of 
Mixtures.  The  thermal  capacity  of  a  body  (solid,  liquid, 
or  gaseous)  is  the  number  of  calories  (see  Def.,  page  100) 
necessary  to  raise  its  temperature  1°.  The  process  of 
measuring  quantities  of  heat,  for  example,  the  thermal 
capacity  of  a  body,  is  called  calorimetry.  One  of  the 
methods  of  calorimetry,  called  the  method  of  mixtures,  is 
very  common,  and  is  that  which  you  will  employ  in 
your  work  in  calorimetry.  The  method  of  mixtures 
consists  essentially  in  putting  the  body  to  be  tested,  after 
its  weight  and  temperature  have  been  noted,  into  a  quan- 
tity of  water  of  known  weight,  whose  temperature  is 
known  but  is  different  from  that  of  the  body.  The 
resulting  common  temperature,  known  as  the  temperature 
of  the  mixture,  is  noted. 


CALOKIMETRY.  103 

The  body  may  be  a  solid,  so  that  it  and  the  water  could 
not  be  literally  mixed.  It  is  customary,  however,  to  refer 
to  a  solid  and  the  water,  when  put  together  in  one  vessel, 
as  the  mixture. 

Experiment  49.  To  find,  by  the  method  of  mixtures, 
the  amount  of  heat  given  out  by  lg  of  lead  in  cooling  1°. 

Apparatus.  Lead  shot ;  a  copper  dipper  to  heat  the  shot  in ;  a 
copper  boiler  ;  a  thermometer ;  a  calorimeter  (this  is  a  tall  cup  of 
nickle-plated  brass,  brightly  polished) ;  a  platform  balance  ;  a  little 
ice-water  a  100CC  graduate  ;.  a  piece  of  cardboard  to  cover  the 
dipper. 

Directions.  Into  the  dipper  put  500g  of  shot.  Cover 
the  top  of  the  dipper  with  the 
cardboard,  in  order  to  keep  the 
shot  from  being  cooled  by  air 
currents.  Through  a  hole  in 
the  cardboard  pass  the  ther- 
mometer and  plunge  its  bulb 
into  the  shot.  In  the  boiler 
place  the  dipper  with  its  flange 
resting  on  the  top  (Fig.  35). 
In  order  that  there  may  be  no 
danger  of  boiling  the  water  in 
the  boiler  all  away,  have  the 
water  reach  nearly  to  the  bot- 
tom of  the  dipper  at  the  start. 
Close  the  side  tube  of  the 
boiler  with  a  stopple,  so  that  Fl»-  35. 

the  steam   will  have   to  pass    out   under   the  flange  of 
the  dipper. 


104  EXPERIMENTAL   PHYSICS. 

While  the  shot  are  heating,  wipe  and  weigh  the  calo- 
rimeter (pronounced  calo-rimfe-ter),  and  measure  out  100g 
of  water  whose  temperature  is  6°  or  8°  colder  than  the  air 
of  the  room,  that  is,  6°  or  8°  below  the  temperature  as 
indicated  by  a  thermometer  near  the  spot  where  the 
experiment  is  to  be  performed.  Pour  the  water  into 
the  calorimeter,  and  place  it  conveniently  near  the  heat- 
ing apparatus,  but  shielded  from  the  heat. 

When  the  temperature  of  the  shot  has  become  practi- 
cally constant,  that  is,  about  100°,  remove  the  thermom- 
eter, and  allow  it  to  cool  till  the  column  stands  at  about 
50°  or  40°.  Then  put  the  thermometer  into  the  calo- 
rimeter, stir  the  water  and  give  the  thermometer  time 
to  come  to  the  temperature  of  the  water.  Record  the 
temperature  of  the  water.  Meanwhile,  stir  the  shot  fre- 
quently with  an  iron  rod  or  any  convenient  object.  Then 
take  the  thermometer  out  of  the  water.  Take  the  dipper 
from  the  boiler,  remove  the  cardboard  (no  time  should  be 
lost  in  this  part  of  the  experiment,  for  the  dipper  and  its 
contents  after  being  taken  from  the  boiler  immediately 
begin  to  cool),  taking  care  to  spill  neither  shot  nor  water, 
very  quickly  pour  the  shot  into  the  calorimeter.  (This  can 
be  successfully  done  by  the  student,  if  he  has  practised 
beforehand  pouring  some  shot  from  a  dipper  into  an  empty 
calorimeter.)  At  once  stir  the  mixture  of  shot  and 
water  quickly  and  thoroughly  with  the  thermometer. 
Record  the  reading  of  the  thermometer  as  soon  as  the 
shot  and  water  have  reached  a  common  temperature, 
which  will  probably  be  a  few  degrees  above  the  temper- 
ature of  the  room.  It  is  of  importance  to  get  this  tem- 
perature accurately.  With  vigorous  stirring  it  takes  but 


CALORIMETRY.  105 

a  few  seconds  for  the  water  and  the  lead  to  reach  a  com- 
mon temperature.  Glance  at  the  thermometer  column 
frequently ;  after  the  first  somewhat  violent  fluctuations 
the  mercury  will  become  stationary  for  an  instant  and 
then  begin  to  fall  slowly ;  the  reading  of  the  column,  at 
the  instant  when  it  becomes  stationary,  is  the  one  to  be 
noted. 

From  the  data  obtained  answer  the  following  questions : 

(1)  If  x  denotes  the  amount  of  heat  given  out  by  lg  of 
lead  in  falling  1°,  how  much  heat  would  be  given  out  by 
the  whole  mass  of  lead  in  falling  1°? 

(2)  How  much  heat  would  be  given  out  by  the  whole 
mass  of  lead  in  falling  from  the  temperature  it  had  when 
it  entered  the  water  to  the  temperature  of  the  mixture  ? 

(The  heat  given  out  by  the  lead  warmed  the  calorimeter  and  the  water 
in  it.     Both  the  water  and  the  calorimeter  had  the  same  temperature.) 

(3)  How  much  heat  does  it  take  to  raise  lg  of  water 
1°?     (See  Def.,  page  100.) 

(4)  How  much  heat  does  it  take  to  raise  the  whole 
mass  of  water  1°? 

(5)  How  much  heat  does  it  take  to  raise  the  whole 
mass  of  water  from  the  temperature  it  had  when  the  shot 
were  poured  in  to  the  temperature  of  the  mixture  ? 

(6)  If  it  takes  0.1  of  a  calorie  to  raise  lg  of  the  sub- 
stance of  which  the  calorimeter  is  made  1°,  how  much 
heat  will  it  take  to  raise  the  temperature  of  the  whole 
calorimeter  1°  ? 

(7)  How  much  heat  will  it  take  to  raise  the  whole 
calorimeter  from  its  temperature  when  the  shot  entered 
to  the  temperature  of  the  mixture  ? 


106  EXPERIMENTAL   PHYSICS. 

When  you  have  answered  the  questions,  make  an  equa- 
tion. On  one  side  put  the  expression  [the  answer  to  (2)] 
for  the  quantity  of  heat  given  out  by  the  lead  in  cooling  ; 
on  the  other,  the  quantity  of  heat  received  by  the  water 
[the  answer  to  (5)]  plus  the  quantity  of  heat  received  by 
ibhe  calorimeter  [the  answer  to  (7)].  On  solving  this 
equation,  you  will  get  the  amount  of  heat  given  out  by 
lg  of  lead  in  cooling  1°. 

A  special  name  is  given  to  the  numerical  value  of  the 
amount  of  heat  yielded  by  lg  of  a  substance  when  its 
temperature  falls  1°.  This  value  is  called  the  specific 
heat  of  the  substance.  The  amount  of  heat  necessary 
to  raise  lg  of  a  substance  1°  is  equal  to  the  amount  of 
heat  given  out  by  lg  of  the  substance  when  its  tempera- 
ture falls  1° ;  hence, 

Definition.  The  specific  heat  of  a  substance  is  the  numer- 
ical value  of  the  thermal  capacity  of  I9  of  the,  substance. 

NOTE.  The  answer  to  (6)  is  called  the  water  equivalent  of  the  calori- 
meter. Why  ? 

QUESTIONS.  What  is  the  specific  heat  of  water  ?  of  the  calorimeter  ? 
What  was  the  thermal  capacity  of  the  lead  used  in  the  preceding  experi- 
ment ?  of  the  water  ?  of  the  calorimeter  ? 


EXAMPLES. 

1.  Into  110s  of  water  at  15°,  contained  in  a  vessel  the  thermal  capacity 
of  which  is  equal  to  that  of  10s  of  water,  are  put  200s  of  a  certain  solid 
at  100°,  and  the  resulting  temperature  of  the  whole  is  25°.  Compute  the 
specific  heat  of  the  solid. 

Solution.     Let  x  denote  the  specific  heat  of  the  solid. 
Then  200  (100  —  25)  x  =  the  number  of  calories  given  out  by  the  lead 
in  cooling  from  100°  to  25°. 


CALOBIMETKY.  107 

110  (25  —  15)  =  the  number  of  calories  received  by  the  water 
in  having  its  temperature  raised  from  15° 
to  25°. 

10  (25  —  15)  =  the  number  of  calories  received  by  the  calo- 
rimeter in  having  its  temperature  raised  from 
15°  to  25°. 

Now  the  number  of  calories  given  out  by  the  lead  were  received 
by  the  water  and  the  calorimeter,  so  we  can  add  together  the  calories 
received  by  the  water  and  the  calorimeter  and  form  an  equation  by 
putting  this  sum  equal  to  the  number  of  calories  given  out  by  the  lead  ; 
that  is, 

200  (100  —  25)  x  =  110  (25  -  15)  +  10  (25  —  15). 

Solving  this  equation,  we  have  x  =  0.08. 

2.  A  coil  of  copper  wire  weighing  45.  Is  was  dropped  into  a  calorimeter 
containing  52. 5s  of  water  at  10°.     The  copper  before  immersion  was  at 
99°. 6,  and  the  common  temperature  of  copper  and  water  after  immersion 
was  16°.  8.      Find  the  specific  heat  of  the  copper  wire. 

NOTE.  When  nothing  is  said  about  the  weight  of  the  calorimeter,  as 
in  the  example  just  given,  make  no  account  of  the  calorimeter  in  the 
computation. 

3.  Find  the  specific  heat  of  a  substance  lOOe  of  which  at  90°,  when 
immersed  in  250s  of  water  at  12°,  gives  a  resulting  temperature  of  18°. 

4.  Compute  the  specific  heat  of  silver  from  the  following  data  : 

Weight  of  silver  =  10.2s  • 

Weight  of  water  =  84s 

Temperature  of  silver  =  102° 

Initial  temperature  of  water  =  11°.  08 
Temperature  of  mixture        =  11°.  69 

5.  If  the  specific  heat  of  mercury  is  0.0333,  what  will  be  the  temper- 
ature of  100s  of  water  taken  at  0°,  into  which  1000&  of  mercury  at  100° 
are  poured  and  thoroughly  stirred  ? 

Solution.     Let  t°  denote  the  required  temperature. 

Then  1000  (100  —  t)  0.0333  =  number  of  calories  of  heat  given  out  by 

mercury  in  cooling  from  100°  to  t°. 

100  (t  —  0)  =  number  of  calories  of  heat  received  by 

the  water   in    having    its  temperature 
raised  from  0°  to  t°. 


108  EXPERIMENTAL   PHYSICS. 

These  two  quantities  of  heat  are  equal,  hence  we  form  the  equation 

1000  (100  -  t)  0.0333  =  100  (t  —  0). 
On  solving  this  equation,  t  =  25°  (nearly). 

6.  Equal  volumes  of  turpentine  at  70°  and  of  alcohol  at  10°  are 
mixed  ;  find  the  resulting  temperature.  (Specific  gravity  of  turpentine, 
0.87;  of  alcohol,  0.80.  Specific  heat  of  turpentine,  0.47;  of  alcohol, 
0.62.) 

LATENT    HEAT. 

46.  Change  of  State.  Every  substance  with  which 
we  are  acquainted  must  be  in  one  of  the  three  states,  or 
forms,  the  solid,  the  liquid,  or  the  gaseous.  Sometimes 
we  find  a  substance  in  the  solid  state,  sometimes  in  the 
liquid  state,  and  sometimes  in  the  gaseous.  For  example, 
water  is  a  substance  with  which  we  are  acquainted  in  the 
solid  state  (as  ice),  in  the  liquid  state,  and  in  the  gaseous 
state  (as  steam).  When  a  solid,  such  as  ice,  melts,  it  passes 
from  the  solid  state  into  the  liquid.  The  solid  is  said  to 
have  undergone  a  change  of  state.  On  the  other  hand, 
when  a  liquid,  like  water,  freezes,  it  has  passed  from  the 
liquid  *to  the  solid  state.  In  this  case  also  a  change  of 
state  has  taken  place.  When  a  liquid,  like  water,  passes 
into  the  gaseous  form,  as  steam,  or  when  the  gas  con- 
denses, or  passes  back  to  a  liquid,  there  is  also  a  change 
of  state.  In  brief,  then,  when  a  substance  passes  from 
one  of  these  states  to  another,  a  change  of  state  is  said  to 
have  taken  place. 

The  next  three  experiments  deal  with  change  of  state. 

Experiment  5O.  To  find  what  changes  in  temperature 
are  produced  by  applying  heat  to  equal  weights  of  ice  and 
ice-water,  contained  in  separate  vessels. 


LATENT    HEAT.  109 

Apparatus.  Two  similar  beakers  ;  a  small  pan  about  3  inches 
deep ;  a  thermometer  ;  a  Bunsen  burner  ;  a  retort-stand  and  ring  ; 
ice  ;  a  platform  balance. 

Directions.  Fill  one  beaker  two-thirds  full  of  small 
pieces  of  ice,  and  put  into  the  other  an  equal  weight  of  ice- 
water.  In  the  pan  of  boiling  water  that  you  have  just 
removed  from  the  flame,  put  both  beakers,  after  noting 
the  temperature  of  each.  Without  putting  the  pan  over 
the  flame  again,  stir  the  ice  almost  constantly,  and  occa- 
sionally stir  the  water  in  the  other  beaker.  Let  the 
beakers  stand  in  the  hot  water  till  nearly  all  the  ice  has 
melted,  then  quickly  note  the  temperature  of  each. 

Both  beakers  are  of  the  same  size  and  have  stood  in  the 
hot  water  for  the  same  length  of  time. 

In  which  one  does  the  temperature  remain  unchanged, 
or  almost  unchanged  ? 

As  both  beakers  were  at  the  same  or  nearly  the  same 
temperature  at  the  start,  what  has  become  of  the  heat 
that  went  to  the  beaker  in  which  the  temperature  rose 
the  least? 

In  what  state  were  the  contents  of  this  beaker  before 
it  was  put  into  the  hot  water  ? 

In  what  state  were  the  contents  after  it  had  been  sub- 
jected to  heat? 

Definition.  The  heat  required  by  substances  for  changing 
their  state  is  called  latent  heat. 

A  better  name  is  heat  effusion,  when  the  change  is  from 
solid  to  liquid  ;  heat  of  vaporization,  when  the  change  is 
from  liquid  to  vapor.  Heat  of  fusion  is  sometimes  called 
latent  heat  of  melting. 


110  EXPERIMENTAL   PHYSECS. 

Definition.  The  heat  that  is  used  in  raising  the  temper- 
ature of  a  body  is  called  sensible  heat,  as  it  can  be  perceined 
by  the  sense  of  touch. 

Experiment  51.  To  find  the  amount  of  heat  necessary 
to  change  la  of  ice  whose  temperature  is  0°  into  1s  of  water 
whose  temperature  is  0°. 

Apparatus.  A  calorimeter  ;  a  platform  balance  ;  a  thermometer; 
a  piece  of  cardboard  to  cover  calorimeter ;  clear  ice. 

Directions.  Record  the  weight  of  the  calorimeter. 
Put  into  the  calorimeter  20 Og  of  water  whose  temperature 
is  about  55°.  Cover  the  calorimeter  with  the  piece  of 
cardboard,  having  a  notch  at  one  side  to  admit  the  ther- 
mometer. (The  cardboard  retards  the  evaporation  of  the 
water.)  Take  a  lump  of  clear  ice  weighing  from  140g  to 
150g,  which  should  have  been  selected  before  the  warm 
water  was  put  into  the  calorimeter,  and  in  an  ice-cutting 
machine  or  in  a  cold  box  break  it  up  quickly  into  pieces 
about  as  large  as  chestnuts.  Use  neither  snow  nor  snow- 
ice.  Record  the  temperature  of  the  water  after  stirring, 
and  immediately,  avoiding  the  wetter  portions,  put  into 
the  calorimeter  about  100g  of  the  ice.  Do  not  weigh  out 
100g  of  crushed  ice,  but  estimate  the  amount  as  nearly  as 
you  can.  Stir  thoroughly,  though  not  violently,  with  the 
thermometer.  As  the  last  particles  of  ice  melt,  record  the 
temperature  indicated  by  the  thermometer.  If  so  much 
ice  has  been  put  in  as  to  cool  the  water  below  5°,  dip  out 
the  ice  which  remains  unmelted,  taking  out  as  little  water 
as  possible.  Weigh  the  calorimeter  and  contents  to  find 
the  weight  of  ice  melted. 


LATENT    HEAT.  Ill 

By  means  of  the  data  obtained  answer  the  following 
questions,  which  indicate  the  course  of  reasoning  that  must 
be  gone  through  in  order  to  find  the  number  of  calories 
necessary  to  melt  lg  of  ice  without  changing  its  temperature. 

(1)  If  x  denotes  the   number  of  calories  required  to 
melt  1s  of  ice,  how  many  calories  are  necessary  to  melt  the 
whole  weight  of  ice  ? 

(2)  How  much  heat  is  required  to  raise  the  temper- 
ature of  lg  of  water  1°?     (See  Def.,  page  100.) 

(3)  How  many  calories  are  required  to  raise  the  tem- 
perature of  the  liquefied-  ice  (ice-water)  from  0°  to  the 
temperature  of  the  mixture  ? 

(4)  How  much  heat  is  given  out  by  lg  of  water  in 
cooling  1°?     (See  Def.,  page  101.) 

(5)  How  many  calories  are   given   out  by  the  warm 
water  in  cooling  to  the  temperature  of  the  mixture  ? 

(6)  In  cooling  1°,  what  part  of  a  calorie  is  given  out  by 
lg  of  the  substance  of  which  the  calorimeter  is  made? 

(The  specific  heat  of  the  calorimeter  is  0.1.) 

(7)  How  many  calories   are   given  out  by  the  whole 
calorimeter  in  cooling  1°? 

(8)  How  many  calories  are  given  out  by  the  calorimeter 
in  cooling  from  its  first  temperature  to  the  temperature  of 
the  mixture  ? 

(The  first  temperature  of  the  calorimeter  is  the  same  as  that  of  the 
water  in  it  at  the  start.) 

Make  an  equation,  putting  on  one  side  the  quantity  of 
heat  necessary  to  melt  the  ice  [answer  to  (1)]  plus  the 
quantity  of  heat  necessary  to  raise  the  ice-water  to  the 
temperature  of  the  mixture  [answer  to  (3)]  ;  on  the  other, 


112  EXPERIMENTAL  PHYSICS. 

put  the  quantity  of  heat  given  out  by  the  water  in  cooling 
to  the  temperature  of  the  mixture  [answer  to  (5)]  plus  the 
quantity  of  heat  given  out  by  the  calorimeter  in  cooling 
to  the  same  temperature  [answer  to  (8)].  On  solving  this 
equation  you  will  get  the  quantity  of  heat  necessary  to 
melt  lg  of  ice. 

Definition.  The  latent  heat  of  fusion  of  a  substance  is 
the  number  of  units  of  heat  required  to  change  1°  of  the 
substance  at  its  melting-point  into  liquid  at  the  same  temper- 
ature. 

How  many  units  of  heat  are  required  to  melt  lg  of  ice  ? 

How  many  units  of  heat  will  be  given  out  by  lg  of  ice- 
water  in  freezing  ? 

Which  takes  the  more  heat,  to  melt  lg  of  ice,  or  to 
raise  the  temperature  of  lg  of  water  from  0°  to  100°? 

EXAMPLES. 

1.  From  the  following  experimental  data  find  the  latent  heat  of  water : 

Weight  of  water  =  200s. 

Temperature  of  water  =  58°. 

Weight  of  ice  =  118s. 

Temperature  of  mixture  when  all  the  ice  was  melted  =  8°. 

(Latent  heat  of  water  is  another  name  for  latent  heat  of  melting.) 

Solution.     Let  x  denote  the  number  of  calories  necessary  to  melt  IK 
of  ice. 

r 

Then  118  x  =  number  of  calories  necessary  to  melt  the  whole 

weight  of  ice. 
118    (8  —  0)  =  number  of  calories  necessary  to  raise  the  liquefied 

ice  from  0°  to  8°. 

200  (58  —  8)  =  number  of  calories  given  out  by  the  warm  water 
in  cooling  from  58°  to  8°. 


LATENT    HEAT.  113 

Now  the  number  of  calories  received  by  the  ice  in  melting  and  by  the 
liquefied  ice  in  having  its  temperature  raised  from  0°  to  8°  was  given  out 
by  the  warm  water  when  its  temperature  fell  from  58°  to  8° ;  in  other 
words,  the  heat  given  out  by  the  warm  water  in  cooling  went  to  melt 
the  ice  and  to  raise  the  temperature  of  the  liquefied  ice,  so  we  have  the 
equation 

118  x  +  118  (8  -  0)  =  200  (58  -  8). 
.-.  x  —  76.7  calories. 

2.  As  the  result  of  experiment,  it  is  found  that  25s  of  copper  at  the 
temperature  of  100°  are  just  sufficient  to  melt  2.875s  of  ice  at  0°,  so  that 
the  water  and  the  copper  are  finally  at  0°.     Taking  80  calories  as  the 
latent  heat  of  water,  from  these  data  find  the  specific  heat  of  copper. 

3.  What  quantity  of  water  at  15°  will  be  required  to  melt  1000s  of  ice 
at  0°,  so  that  the  resulting  mixture  shall  be  at  5°  ?     (Take  the  latent  heat 
of  water  as  80.) 

Experiment  52.  To  find  the  number  of  calories  P  of 
steam,  whose  temperature  is  100°,  gives  up  in  changing  into 
water  at  100°. 

Apparatus.  A  calorimeter  ;  a  thermometer  ;  a  "  trap"  (consisting 
of  a  side-necked  test-tube  with  a  perforated  stopple,  through  which, 
and  reaching  nearly  to  the  bottom  of  the  test-tube,  a  piece  of  glass 
tube  is  thrust) ;  a  copper  boiler  with  a  cone  (or  better  a  sterilizing 
can) ;  a  Bunsen  burner  ;  a  piece  of  cardboard  to  cover  the  calo- 
rimeter (this  cardboard  should  have  a  notch  at  one  edge  to  admit 
the  tube  conducting  the  steam,  and  in  the  middle  a  perforation  to 
admit  the  thermometer)  ;  two  pieces  of  rubber  tube,  one  about  50cm 
in  length,  the  other  about  10cm. 

NOTE.  The  object  of  the  trap  is  to  catch  the  water  from  the  steam 
that  is  condensed,  when  it  passes  from  the  boiler  through  the  long  tube  ; 
the  steam  must  pass  through  a  long  tube  in  order  to  keep  the  calorimeter 
a  long  distance  from  the  Bunsen  burner,  otherwise  the  contents  of  the 
calorimeter  would  have  its  temperature  raised  by  the  heat  of  the  flame. 

Directions.  Fill  the  boiler  one-third  full  of  water. 
Fit  a  cone  tightly  on  the  boiler  (Fig.  36).  Stop  the  open- 
ing in  the  apex  of  the  cone  and  also  the  side  tube  near 


114  EXPERIMENTAL    PHYSICS. 

the  apex.  Over  the  side  tube  of  the  boiler  slip  the  longer 
piece  of  rubber  tube.  Slip  its  other  end  over  the  end  of 
the  glass  tube  that  reaches  to  the  middle  of  the  test-tube. 
Over  the  side  tube  of  the  test-tube  slip  the  short  piece  of 
rubber  tube  with  a  bit  of  glass  tube  in  one  end. 


FIG.  36. 

Record  the  weight  of  the  calorimeter.  Then  weigh  care- 
fully in  the  calorimeter  275g  of  water  whose  temperature 
is  about  15°  below  the  temperature  of  the  room.  When 
the  steam  flows  strongly  through  the  trap,  the  mouth  of 
the  rubber  tube,  attached  to  the  side  tube,  should  be 
plunged  beneath  the  surface  of  the  water  in  the  calorime- 
ter, but  not  so  deep  as  to  prevent  the  steam  from  con- 
densing with  a  very  audible  sound.  Cover  the  calorimeter 
with  the  cardboard,  and  through  the  opening  pass  the 


LATENT    HEAT.  115 

• 

thermometer.  Frequently  stir  the  water  with  the  ther- 
mometer. Screen  the  calorimeter  from  the  heat  radiated 
by  the  flame  and  other  hot  objects.  When,  by  the  con- 
densation of  the  steam,  the  temperature  of  the  water  has 
been  raised  about  15°  above  the  temperature  of  the  room, 
remove  the  tube  from  the  water.  Stir  the  water  thoroughly 
with  the  thermometer  and  take  its  temperature. 

What  was  the  object  in  having  the  final  temperature  of 
the  water  as  much  above  the  temperature  of  the  room  as 
the  initial  temperature  of  the  water  was  below  it  ? 

Weigh  the  calorimeter  and  contents,  and  thus  find  the 
weight  of  the  condensed  steam.  This  weighing  is  very 
important  and  should  be  carefully  done. 

Notice  that  there  are  two  portions  of  heat  yielded  to  the 
cold  water  and  to  the  calorimeter  ;  one  coming  from  the 
steam  during  the  act  of  condensation,  the  other  coming 
from  the  condensed  steam  (water  at  100°)  while  cooling 
to  the  final  temperature. 

In  the  computation  of  the  latent  heat  of  vaporization, 
take  0.1  as  the  specific  heat  of  the  substance  of  which  the 
calorimeter  is  made. 

(1)  If  x  denotes  the  number  of  calories  given  up  by  lg 
of  steam  at  100°  in  changing  into  water  at  100°,  how 
many  calories  are  given  up  by  the  whole  weight  of  the 
steam  during  this  change  ? 

(2)  How  many  calories  are  given  up  by  lg  of  water  in 
cooling  1°?     (See  Def.,  page  101.) 

(3)  How  many  calories  are  given  up  by  the  condensed 
steam  (water  at  100°)  in  cooling  1°? 

(4)  How  many  calories  are  given  up  by  the  condensed 
steam  in  cooling  to  the  temperature  of  the  mixture  ? 


116  EXPERIMENTAL    PHYSICS. 

« 

(5)  How  many  calories  are  required  to  raise  the  temper- 
ature of  lg  of  water  1°  ?     (See  Def.,  page  100.) 

(6)  How  many  calories  are  required  to  raise  the  whole 
weight  of  cold  water  from  its  first  temperature   to  the 
temperature  of  the  mixture  ? 

(7)  How  many  calories  are  required  to  raise  1°  the  tem- 
perature of  lg  of  the  substance  of  which  the  calorimeter 
is  made? 

(8)  How  many  calories  are  required  to  raise  the  temper- 
ature of  "the  whole  calorimeter  1°? 

(9)  How  many  calories  are  required  to  raise  the  calo- 
rimeter from  its  first  temperature  (the  temperature  of  the 
water  at  first)  to  the  temperature  of  the  mixture  ? 

Make  an  equation,  putting  on  one  side  the  quantity  of 
heat  given  up  by  the  steam  in  changing  into  water  [answer 
to  (1)]  plus  the  quantity  of  heat  given  up  by  the  condensed 
steam  in  cooling  to  the  temperature  of  the  mixture  [answer 
to  (4)] ;  on  the  other,  the  quantity  of  heat  necessary  to  raise 
the  cold  water  from  its  first  temperature  to  that  of  the 
mixture  [answer  to  (6)]  plus  the  quantity  of  heat  required 
to  raise  the  calorimeter  from  its  first  temperature  to  the 
temperature  of  the  mixture '[answer  to  (9)].  On  solving 
this  equation  you  will  get  the  quantity  of  heat  given  up 
by  lg  of  steam  in  changing  into  water. 

How  many  calories  would  be  required  to  change  lg  of 
water  whose  temperature  is  100°  into  steam  whose  temper- 
ature is  100°  ? 

Which  would  give  out  the  greater  amount  of  heat, 
lg  of  steam  whose  temperature  is  100°  in  changing  into 
water,  or  lg  of  water  in  cooling  from  100°  to  0°? 


LATENT  HEAT.  117 


QUESTIONS  AND  EXAMPLES. 

1.  Why  is  steam  such  an  effective  agent  in  heating  buildings  ? 

SUGGESTION.  Consider  the  amount  of  heat  given  out  by  steam  in 
condensing. 

2.  Beginning  with  the  fire  beneath  the  steam  boiler,  describe  as  fully 
as  you  can  the  transferences  of  heat  that  occur  in  the  process  of  heating  a 
room  by  means  of  coils  of  steam-pipe. 

3.  Using  as  a  model  the  definition  of  the  latent  heat  of  fusion,  page 
112,  state  a  definition  for  the  latent  heat  of  vaporization. 

4.  From  the  results  of  the  following  experiment,  allowing  for  the  heat 
absorbed  by  the  brass  calorimeter,  compute  the  latent  heat  of  steam  (the 
latent  heat  of  vaporization) : 

Weight  of  calorimeter  =  326. 3s. 

Weight  of  calorimeter  and  water  =  757.7s. 

Weight  of  steam  condensed  =  46.35s. 

Temperature  of  steam  =  100°. 

Temperature  of  water  before  experiment  =  7°.  5. 

Temperature  of  water  after  experiment  =  62°.  5. 

Specific  heat  of  brass  =  0.09. 

5.  A  vessel  containing  30s  of  ice  is  placed  over  a  Bunsen  burner  ;  how 
many  calories  will  be  required  to  melt  the  ice  and  to  vaporize  the  water 
completely  ?    (Latent  heat  of  fusion,  80  ;  latent  heat  of  vaporization,  536.) 

47.  Freezing-Mixtures.  When  ice  melts,  heat  dis- 
appears. The  form  of  the  ice  is  changed  from  the  solid 
to  the  liquid,  but  there  is  no  marked  rise  in  temperature 
till  all  the  ice  has  vanished.  The  heat  that  has  dis- 
appeared in  this  process  has  gone  to  change  the  form  of 
the  substance,  without  appreciably  raising  the  temperature 
of  the  water  as  long  as  any  of  the  ice  remains.  When  ice 
melts,  heat  passes  from  surrounding  objects  that  have  a 
higher  temperature  than  that  of  the  ice  to  the  ice  itself  ; 
consequently,  those  objects  which  in  this  manner  part  with 


118  EXPERIMENTAL    PHYSICS. 

heat  must  become  colder,  unless  heat  is  constantly  supplied 
to  them.  When  salt  is  mixed  with  ice  the  ice  melts  more 
quickly  and  so  takes  heat  more  rapidly  from  surrounding 
objects.  A  mixture  of  ice  and  salt  is  called  a  freezing- 
mixture.  When  this  mixture  surrounds  a  freezer  full  of 
cream,  the  cream  freezes.  The  mixture  in  becoming  liquid 
has  taken  heat  from  the  cream,  and  the  cream  has  frozen. 
Is  the  freezing-mixture  colder  than  the  cream?  This  is 
a  pertinent  question  which  the  following  experiment  will 
enable  you  to  answer. 

Experiment  53.  To  find  whether  the  temperature  of  a 
mixture  of  melting  ice  and  salt  is  different  from  that  of  melt- 
ing ice. 

Apparatus.  A  beaker  ;  a  thermometer  ;  a  platform  balance  ; 
snow  or  broken  ice  ;  salt. 

Directions.  Mix  in  the  beaker  one  part  by  weight  of 
salt  and  two  parts  by  weight  of  snow  or  broken  ice.  Put 
a  thermometer  into  the  mixture,  and  note  the  temperature. 

What  conclusion  do  you  reach  ? 

THERMOMETRIC    SCALES. 

48.    Centigrade,  Fahrenheit,  and  Reaumur    Scales. 

Besides  the  Centigrade  scale,  with  which  you  have  become 
familiar,  there  are  two  others  :  the  Fahrenheit,  in  use  in 
England  and  the  United  States,  and  the  Reaumur,  in  use 
in  Russia  and  a  few  places  in  the  north  of  Germany.  The 
Fahrenheit  scale,  named  for  Fahrenheit,  of  Dantzig  in 
Germany,  who  about  1714  was  the  first  to  construct 
thermometers  whose  readings  were  the  same  when  put 


THERMOMETR1C    SCALES. 


119 


into  substances  having  the  same  temperature,  has  for  its 
zero-point  the  temperature  of  a  mixture  of  snow  and  salt. 
On  this  scale  the  freezing-point  is  32°  and  the  boiling- 
point  212°.  On  the  Reaumur  scale  the  freezing-point  is 
marked  0,  just  as  on  the  Centigrade  scale,  but  the  boiling- 
point  is  marked  80. 

Occasionally  you  will  be  required,  when  given  the  read- 
ing  of   one   of  these   scales,  to    find   the    corresponding 
reading  of  "one  of  the  others.     The  follow-      Q      R.     F 
ing  table  will  help  you  to  understand  how 
this  can  be  done. 

C.  F.          R. 

Freezing-point       0  32  0 

Boiling-point     100         212         80 

C.  stands  for  Centigrade,  F.  for  Fahrenheit, 
and  R.  for  Reaumur. 

Between  the  fixed  points  on  the  Centi- 
grade scale  (Fig.  37)  there  are  100  equal 
parts ;  on  the  Fahrenheit,  180 ;  on  the 
Reaumur,  80.  Hence  a  change  of  5°  C.  is 
equivalent  to  a  change  of  9°  F.,  or  1°  C.  is 
equal  to  |°  F.  Fahrenheit's  zero  is  32° 
below  the  freezing-point.  Hence,  to  re- 
duce Fahrenheit  readings  to  Centigrade 
readings  subtract  32  from  the  number  of 
Fahrenheit  degrees  and  multiply  the  remainder  by  |. 
(7=f  (J--82). 

To  reduce  Centigrade  readings  to  Fahrenheit,  multiply 
the  number  of  Centigrade  degrees  by  -|  and  add  32. 
JF=£  6^+32. 


FIG.  37. 


f 

120  EXPERIMENTAL    PHYSICS. 

EXAMPLES. 

1.  Show  by  a  process  of  reasoning  similar  to  that  just  given  that 

E  =  f  (F  —  32) 
F  =  I  R  +  32 

2.  Show  that 


3.  Find  the  corresponding  temperatures  on  the  Centigrade  scale  of 
the  following  melting  points  : 

Lead,  626°  F.;  bismuth,  508°  F.;  tin,  442°  F.;  Rose's  metal,  200°  F. 
NOTE.     Rose's  metal  is  an  alloy  of  the  first  three. 

4.  Find  the  equivalents  on  the  Reaumur  scale  of  the  following  temper- 
atures : 

Usual  temperature  of  the  human  body  =    98°.4  F. 
"  "  "  a  common  frog    =    64°     " 

"  "  "  a  chicken  =  111°     " 

5.  In  the  expedition  to  China  in  1829  the  Russian  army  experienced 
for  several  days  a  temperature  of  —32°.  8  R.     What  would  this  be  on 
the  Fahrenheit  scale  ? 

6.  The  absolute  zero1  is  —273°  C.     What  is  this  on  the  Fahrenheit 
scale  ? 

7.  At  what  temperature  is  the  reading  of  the  Centigrade  identical 
with  that  of  the  Fahrenheit  ? 


FORMATION    AND    CONDENSATION    OF    VAPOR. 

49.  Evaporation ;  Boiling*.  The  object  of  the  next 
two  experiments  is  to  bring  out  the  distinction  between 
evaporation  and  boiling. 

Experiment  54.  To  find  whether  vapor  will  form  quietly 
at  the  surface  of  water. 

Apparatus.  A  large  test-tube  ;  a  Bunsen  burner  ;  a  small  piece 
of  window-glass. 

1  See  page  94. 


FORMATION    AND   CONDENSATION   OF   VAPOR.       121 


Directions.  Hold  the  test-tube,  half  filled  with  water, 
above  the  flame,  and  warm  the  water,  but  do  not  let  it 
boil.  Above  the  mouth  of  the  test-tube,  and  at  a  little 
distance  from  it,  hold  the  glass  plate,  which  should  be 
cold,  or  the  experiment  may  fail. 

How  did  the  particles  of  water  which  you  see  get  on  the 
piece  of  glass  ? 

If  the  piece  of  glass  had  not  been  held  over  the  mouth 
of  the  test-tube,  what  would  have  become  of  the  water 
which  now  adheres  to  the  glass  ? 

If  the  test-tube  were  allowed  to  remain  uncovered,  what 
would  become  of  the  water  in  it  after  a  time  ? 

Definition.  Evaporation  is  the  quiet  formation  of 
vapor  at  the  surface  of  a  liquid. 

Experiment  55.  To  find 
what  phenomena  occur  when 
water  is  heated  gradually  to 
boiling. 


Apparatus.  A  test-tube,  provided 
with  a  small  side  tube,  fitted  with  a 
perforated  stopple  with  a  glass  tube 
thrust  through,  which  reaches  almost 
to  the  bottom  of  the  test-tube ;  a 
bit  of  rubber  tube  to  fit  the  side 
tube ;  a  tumbler  ;  a  Bunsen  burner  ; 
a  piece  of  glass  tube,  bent  at  right 
angles,  slipped,  as  shown  in  Fig.  38, 
into  one  end  of  the  rubber  tube ;  a 
clasp  with  which  to  attach  the  test- 
tube  to  the  tumbler. 


FIG.  38. 


Directions.     Draw  some  cold  water  from  the  tap,  and 
fill  the  test-tube  nearly  to  a  level  with  the  side  tube.     Put 


122  EXPERIMENTAL    PHYSICS. 

the  stopple  with  its  tube  in  place  in  the  mouth  of  the  test- 
tube.  Clasp  the  test-tube  to  the  tumbler.  Let  the  end 
of  the  glass  tube,  which  you  should  attach  to  the  side  tube 
by  means  of  the  rubber  tube,  dip  lcm  or  2cm  beneath  the 
cold  water,  which  should  nearly  fill  the  tumbler.  By 
applying  heat  to  the  bottom  of  the  test-tube,  gradually 
warm  the  water. 

Before  the  water  boils,  bubbles  appear  in  the  test-tube. 

Do  these  bubbles  rise  to  the  top  of  the  water  in  the 
test-tube  ? 

Are  they  bubbles  of  steam  ? 

(It  may  be  best  to  suspend  judgment  for  a  little  while  before  answering 
this  question.) 

Do  they  burst  at  the  surface  ? 

Are  they  large  or  small  ? 

As  the  water  becomes  warmer,  more  bubbles  form. 

In  what  part  of  the  vessel  do  they  form  ? 

Do  they  rise  to  the  surface  of  the  water  in  the  test-tube  ? 

As  they  rise,  do  they  grow  larger  or  smaller  ? 

Are  they  bubbles  of  steam  ? 

(It  may  be  best  to  suspend  judgment  for  a  little  while  before  answering 
this  question.) 

In  the  upper  part  of  the  test-tube,  is  the  water  warmer 
or  colder  than  at  the  bottom? 

If  there  is  a  change  of  size  in  these  bubbles  as  they  rise, 
how  do  you  account  for  it? 

Do  any  bubbles  appear  at  the  end  of  the  glass  tube  in 
the  beaker  of  water?  (When  bubbles  begin  to  appear 
in  the  beaker  at  the  mouth  of  the  tube,  watch  them 
carefully.) 


FORMATION   AND   CONDENSATION   OF   VAPOR.       123 

As  the  water  in  the  test-tube  gets  still  warmer,  do 
bubbles  rise  to  the  surface  in  either  vessel? 

How  do  you  account  for  the  sharp  rattling  noise  (which 
is  called  singing  or  simmering)  that  is  heard  just  before 
the  water  in  the  test-tube  is  brought  to  boiling  ? 

After  the  bubbles  have  begun  to  come  from  the  glass 
tube  in  the  beaker,  do  they  change  in  character  as  time 
goes  on? 

At  the  close  of  the  experiment,  do  these  bubbles  detach 
themselves  from  the  end  of  the  tube? 

After  reflecting  carefully  on  what  you  have  observed, 
can  you  tell  how  to  distinguish  an  air-bubble  from  a  steam- 
bubble? 

Is  steam  visible  ? 

When  water  is  boiling  in  a  tea-kettle,  what  is  the  little 
cloud  seen  at  the  nose  ? 

Keeping  the  test-tube  in  position  and  letting  the  end  of 
the  glass  tube  rest  on  the  bottom  of  the  beaker,  remove 
the  lamp  and  note  what  happens  as  the  water  begins  to 
cool. 

Do  bubbles  form  ? 

Is  the  water  in  the  test-tube  boiling  ? 

If  the  water  is  not  boiling,  what  is  the  cause  of  what 
you  observe  ? 

Definition.  Boiling  (or  ebullition)  is  the  rapid  formation 
of  vapor  in  the  interior  of  a  liquid. 

Experiment  56.  To  find  the  temperature  at  which  the 
aqueous  vapor  in  the  air  will  condense. 

Apparatus.  A  calorimeter,  brightly  polished  ;  a  thermometer  ; 
ice  or  snow  ;  salt. 


124  EXPERIMENTAL   PHYSICS. 

Directions.  Into  the  calorimeter  pour  water  drawn 
from  the  tap  until  it  is  of  a  depth  sufficient  to  cover 
a  little  more  than  the  bulb  of  the  thermometer.  By 
additions  of  ice-water  or  ice,  with  constant  stirring,  gradu- 
ally cool  this  water  until  the  brightly  polished  surface  of 
the  calorimeter  becomes  dimmed  with  dew.  (Should  no 
dew  appear  when  the  thermometer  reads  0°,  add  salt  and 
ice.)  If  at  any  time  the  water  in  the  calorimeter  becomes 
more  than  5cm  deep,  pour  out  the  extra  water.  Record 
the  temperature  as  soon  as  any  dew  is  seen  to  appear 
on  the  calorimeter.  Then  allowing  the  temperature  of 
the  water  to  rise  gradually  by  receiving  heat  from  the 
room,  record  the  temperature  at  which  the  dew  begins  to 
disappear. 

Care  should  be  taken  not  to  let  the  breath  come  upon 
the  cup,  or  near  it ;  for  the  surface  of  the  cup  would 
become  dimmed  by  the  breath.  By  keeping  some  par- 
ticular spot  of  the  cup  turned  from  you  most  of  the  time, 
and  glancing  at  this  spot  frequently  in  order  to  detect 
the  appearance  or  disappearance  of  dew  upon  it,  you  will 
more  easily  avoid  errors  from  this  source. 

The  average  of  the  two  temperatures  recorded  is  taken 
as  the  dew-point. 

Definition.  The  temperature  at  which  the  air  deposits 
some  of  its  aqueous  vapor  is  called  the  dew-point. 

The  dew-point  depends  upon  the  amount  of  aqueous 
vapor  in  the  air,  and  differs  greatly  from  time  to  time. 
In  general  the  dew-point  is  low  in  winter,  but  high  in 
summer. 


PECULIARITY    IN    THE    EXPANSION    OF    WATER.     125 


PECULIARITY    IN    THE    EXPANSION    OF    WATER 

5O.  Maximum  Density  of  Water.  During  the  proc- 
ess of  lowering  the  temperature  of  water  to  the  freezing- 
point,  the  water  contracts  till  it  reaches  a  certain  tempera- 
ture, and  then  it  begins  to  expand. 

Experiment  57.  To  find  the  temperature  at  which 
water  is  at  its  greatest  density. 

Apparatus.  A  250CC  flask  ;  a  rubber  stopple,  perforated  with  two 
holes,  one  to  admit  a  tube  25cm  long  of  rather  fine  bore  (2mm  or 
;3mm),  the  other  to  admit  a  thermometer  ;  a  very  narrow  rubber  band 
for  a  marker  ;  ice  or  snow. 

Directions.  Avoiding  air-bubbles,  fill  the  bottle  com- 
pletely with  cold  water.  Put 
in  place  the  stopple,  through 
which  you  have  thrust  the  tube 
and  the  thermometer.  The  bulb 
of  the  thermometer  should  oc- 
cupy a  position  midway  between 
the  bottom  of  the  flask  and  its 
top.  Slip  the  marker  over  the 
glass  tube.  After  packing  the 
flask  in  snow  or  broken  ice  as 
shown  in  Fig.  39,  wait  till  the 
thermometer  column  becomes 
stationary.  Bring  the  marker 
to  a  level  with  the  top  of  the 
water  column,  which  should  also 
have  become  stationary.  Then 

take  the  flask  from  the  ice,  and  watch  the  motion  of  the 
water  column  as  the  temperature  rises. 

Before  the  column  begins  to  rise,  does  it  sink  ? 


126  EXPERIMENTAL    PHYSICS. 

If  the  column  sinks,  what  is  the  temperature  of  the 
water  as  indicated  by  the  thermometer  when  the  column 
is  lowest? 

From  the  action  of  the  water  column  and  the  indications 
of  the  thermometer,  what  inference  can  you  draw? 

51.  Results    of  the    Peculiarity  in    the    Expansion 
of  Water  brought   out   by  the   Last  Experiment.     In 

winter  the  surfaces  of  ponds  and  lakes  lose  heat.  The 
water  at  the  surface  being,  bulk  for  bulk,  heavier  than  that 
below,  sinks ;  this  sinking  of  cold  water  goes  on  till  the 
temperature  of  the  whole  pond  is  4°.  The  surface  water 
cools,  but  it  is  now  less  dense  than  the  water  below  ;  this 
less  dense  water,  therefore,  floats,  and  its  temperature  falls 
till  it  freezes.  The  ice,  as  we  know,  floats.  Deep  bodies 
of  water  undisturbed  by  currents  near  the  bottom  or  by 
springs,  like  Lake  Tahoe  in  California,  show  a  tem- 
perature at  the  bottom  of  about  4°  all  the  year  round.  If 
water  did  not  have  this  peculiarity  in  its  expansion,  the 
temperature  of  the  whole  pond  would  be  reduced  to  0°. 
Then,  if  the  water  still  continued  to  contract  on  freezing, 
layer  after  layer  of  ice  would  form  only  to  sink,  until  the 
whole  pond  would  be  a  mass  of  solid  ice. 

In  Art.  6  it  was  stated  that  a  cubic  centimeter  of  water 
weighs  I9  ;  this  statement  should  now  be  amended  to  read 
a  cubic  centimeter  of  water  at  4-°  weighs  la. 

DISCUSSION    OF    A    FEW    TERMS. 

52.  Method.     At  the  end  of  Chapter  I.  the  meaning 
of  observation  and  experiment,  and  the  necessity  of  dis- 
tinguishing between  facts  and  inferences  from  the  facts 


DISCUSSION    OF   A   FEW   TERMS.  127 

were  discussed.  At  this  point  you  should  turn  back  and 
review  pages  62  and  63. 

You  have  already  learned  that  experiment  is  a  most 
fruitful  means  of  ascertaining  facts. 

The  method,  that  is,  the  mode  or  way  of  accomplishing 
an  end,  differs  for  different  experiments ;  but  while 
experiments  are  infinite  in  number,  the  methods  pursued 
in  performing  them  are  few,  so  it  is  possible,  by  marshall- 
ing the  experiments  each  under  its  proper  method,  to 
bring  order  out  of  chaos.  A  most  important  method  is 
known  as  the  method  of  differences.  Its  utility  depends  upon 
varying  only  one  condition  at  a  time,  while  the  precaution 
is  taken  to  keep  all  the  other  conditions  unchanged. 

Interesting  experiments  according  to  the  method  of 
differences  are  not  rare.  "  In  his  discovery  of  the  cause 
of  dew,  Dr.  Wells  made  use  of  this  method.  If  on  a 
clear  calm  night  a  sheet  or  other  covering  is  stretched 
a  foot  or  two  above  the  earth,  so  as  to  screen  the  ground 
from  the  open  sky,  dew  will  be  found  on  the  grass  around 
the  screen  but  not  beneath  it.  As  the  temperature  and 
moistness  of  the  air,  and  other  circumstances,  are  exactly 
the  same,  the  open  sky  must  be  an  indispensable  antecedent 
to  dew.  The  same  experiment  is  indeed  tried  for  us  by 
nature ;  for  if  we  make  observations  of  dew  during  two 
nights  which  differ  in  nothing  but  the  absence  of  clouds  in 
one  and  their  presence  in  the  other,  we  shall  find  that  the 
clear  sky  is  requisite  to  the  formation  of  dew."  l 

53.    Empirical    Knowledge ;    Classified    Knowledge. 

However  useful  empirical  knowledge,  the  knowledge  gained 

1  Elementary  Lessons  in  Logic,  by  W.  Stanley  Jevons,  p.  244, 


128  EXPERIMENTAL    PHYSICS. 

by  experience,  may  be,  its  importance  is  small  as  compared 
with  classified  knowledge,  that  is,  knowledge  well  con- 
nected and  perfectly  explained.  "  He  who  knows  exactly 
why  a  thing  happens  will  also  know  exactly  in  what 
cases  it  will  happen,  and  what  differences  in  the  circum- 
stances will  prevent  the  event  from  happening.  Take,  for 
instance,  the  simple  effect  of  hot  water  in  cracking  glass. 
This  is  usually  learned  empirically.  Most  people  have  a 
confused  idea  that  hot  water  has  a  natural  and  inevitable 
tendency  to  break  glass,  and  that  thin  glass,  being  more 
fragile  than  other  glass,  will  be  more  easily  broken  by  hot 
water.  Physical  science,  however,  gives  a  very  clear 
reason  for  the  effect,  by  showing  that  it  is  only  one  case 
of  the  general  tendency  of  heat  to  expand  substances. 
The  crack  is  caused  by  the  successful  effort  of  the  heated 
glass  to  expand  in  spite  of  the  colder  glass  with  which  it 
is  connected.  But  then  we  shall  see  at  once  that  the 
same  will  not  be  true  of  thin  glass  vessels  ;  the  heat  will 
pass  so  quickly  through  that  the  glass  will  be  nearly 
equally  heated ;  and  accordingly  chemists  habitually  use 
thin  uniform  glass  vessels  to  boil  or  hold  hot  liquids  with- 
out fear  of  fractures  which  would  be  sure  to  take  place  in 
thick  glass  vessels  or  bottles."  * 

54.  Cause ;  Hypothesis.  By  the  cause  of  an  event  we 
mean  the  circumstances  that  must  have  preceded  in  order 
that  the  event  should  happen.  An  event  has  in  general 
more  than  a  single  cause.  "  The  cause  of  the  boiling 
of  water  is  riot  merely  the  application  of  heat  up  to 
a  certain  degree  of  temperature,  but  the  possibility  also 

1  Elementary  Lessons  in  Logic,  by  W.  Stanley  Jevons,  p.  257. 


THE   MOLECULAR    HYPOTHESIS.  129 

of  the  escape  of  the  vapor  when  it  acquires  a  certain 
pressure."  1 

Hypothesis  means  in  science  the  imagining  of  a  cause 
which  underlies  the  phenomena  we  are  examining,  and  is 
the  agent  in  their  production  without  being  capable  of 
direct  observation.  In  making  an  hypothesis  we  assert 
the  existence  of  a  cause  on  the  ground  of  the  facts 
observed,  and  the  probability  of  its  existence  depends 
upon  the  number  of  diverse  facts  it  enables  us  to  explain 
or  reduce  to  harmony. 


THE  MOLECULAR  HYPOTHESIS. 

55.  Molecular  Hypothesis  of  Matter.  The  follow- 
ing brief  account  of  the  molecular  hypothesis  of  matter  in 
its  modern  form  2  may  show  more  clearly  how  an  hypoth- 
esis enables  us  to  harmonize  several  different  facts. 

The  material  substances,  as  air,  metals,  wood,  glass, 
water,  and  so  on,  are  termed  in  the  language  of  physics, 
matter. 

All  matter,  according  to  the  molecular  hypothesis,  is 
supposed  to  consist  of  exceedingly  small  particles,  sepa- 
rated from  each  other  by  spaces.  One  of  these  exceedingly 
small  particles  is  called  a  molecule. 

"  Every  molecule  consists  of  a  definite  quantity  of  matter, 
which  is  exactly  the  same  for  all  molecules  of  the  same 

1  Elementary  Lessons  in  Logic,  by  W.  Stanley  Jevons,  p.  239. 

2  The  molecular  hypothesis  is  a  very  old  one.     Lucretius,  a  Roman  poet 
(95-55  B.C.),  in  his  poem  De  Rerum  Natura  expounds  the  molecular 
hypothesis,  and  shows  us  that  even  in  that  remote  period  philosophers  held 
the  opinion  that  the  observed  properties  of  bodies  apparently  at  rest  are 
due  to  the  action  of  invisible  molecules  in  rapid  motion. 


130  EXPERIMENTAL   PHYSICS. 

substance.  ...  The  molecules  of  all  bodies  are  in  a  con- 
stant state  of  agitation.  The  hotter  a  body  is,  the  more 
violently  are  its  molecules  agitated.  In  solid  bodies,  a 
molecule,  though  in  continual  motion,  never  gets  beyond 
a  certain  small  distance  from  its  original  position  in  the 
body.  The  path  which  it  describes  is  confined  within  a 
very  small  region  of  space. 

"  In  fluids,1  on  the  other  hand,  there  is  no  such  restriction 
to  the  excursions  of  a  molecule.  It  is  true  that  the  mole- 
cule can  generally  travel  but  a  very  small  distance  before 
its  path  is  disturbed  by  an  encounter  with  some  other 
molecule.  ...  In  fluids  the  path  of  the  molecule  is  not 
confined  within  a  limited  region,  as  in  the  case  of  solids, 
but  may  penetrate  to  any  part  of  the  space  occupied  by 
the  fluid."  2 

56.  Evaporation  and  Condensation  explained  by  the 
Molecular  Hypothesis.  The  following  explanation  has 
been  adapted  from  that  given  by  Clerk  Maxwell  in  his 
Theory  of  Heat.  Some  of  the  molecules  of  the  liquid  which 
are  at  the  surface  and  are  moving  from  the  mass  of  the 
liquid  may,  by  being  struck  by  other  molecules,  get  such 
velocities  that  they  will  escape  from  the  forces  which  retain 
the  other  molecules  in  the  liquid,  and  will  fly  about  as 
vapor  in  the  space  outside  the  liquid.  This  is  the  way  in 
which  the  molecular  hypothesis  explains  evaporation.  At 
the  same  time,  a  molecule  of  the  vapor  striking  the  liquid 
may  become  entangled  among  the  molecules  of  the  liquid, 
and  may  thus  become  part  of  the  liquid.  This  is  the 

1  The  term  fluid  includes  liquids  and  gases. 

2  Theory  of  Heat,  bv  J.  Clerk  Maxwell,  p.  306. 


THE   MOLECULAK    HYPOTHESIS.  131 

explanation  which  the  molecular  hypothesis  gives  of 
condensation.  The  number  of  molecules  that  pass  from 
the  liquid  to  the  vapor  depends  on  the  temperature  of  the 
liquid.  The  number  of  molecules  that  pass  from  the 
vapor  to  the  liquid  depends  on  the  density  of  the  vapor 
as  well  as  on  its  temperature.  If  the  temperature  of  the 
vapor  is  the  same  as  that  of  the  liquid,  evaporation  will 
take  place  as  long  as  more  molecules  are  evaporated  than 
condensed ;  but  when  the  density  of  the  vapor  has  in- 
creased so  much  that  as  many  molecules  are  condensed 
as  evaporated,  then  the  vapor  has  attained  its  maximum 
density.  The  vapor  is  then  said  to  be  saturated,  and  it  is 
commonly  supposed  that  evaporation  ceases.  According 
to  the  molecular  hypothesis,  however,  evaporation  is  still 
going  on  as  fast  as  ever  ;  only  condensation  is  also  going 
on  at  an  equal  rate,  since  the  proportions  of  liquid  and 
gas  remain  unchanged. 


EXAMPLES. 

1.  When  the  barometer  is  77.8cm,  what  is  the  error  of  the  boiling- 
point  of  a  thermometer  that  in  freely  escaping  steam  reads  100°.  1  ? 

2.  Explain  why  the  temperature  of  boiling  water  depends  upon  the 
pressure. 

3.  Show  the  steps  in  the  process  of  reasoning  by  which  you  found 
the  coefficient  of  linear  expansion  of  brass  from  the  results  of  your 
experiment. 

4.  When  the  temperature  is  0°,  a  copper  lightning-rod  measures  50  ft. ; 
find  its  length  in  summer  when  heated  to  a  temperature  of  27°.     The 
coefficient  of  linear  expansion  of  copper  is  0.0000173. 

5.  The  coefficient  of  linear  expansion  of  steel  being  0.000012,  what  is 
the  length  at  0°  of  a  bar  that  is  just  lm  long  at  20°  ? 


132  EXPERIMENTAL    PHYSICS. 

6.  A  mass  of  air  at  0°  measures  200™  ;  at  100°  it  measures  27ftcc. 
Provided  both  measurements  were  taken  under  the  same  barometric 
pressure,  find  the  coefficient  of  expansion  of  air. 

7.  When  the  temperature  is  20°,  a  mass  of  oxygen  gas  measures 
500CC.     When  its  temperature  is  raised  to  40°,  what  will  the  volume  of 
the  gas  become  ? 

8.  When  the  pressure  is  38cln  and  the  temperature  is  68°. 25,  a  certain 
mass  of  air  has  a  volume  of  480CC ;  what  will  this  volume  become  when 
the  pressure  is  76cm  and  the  temperature  is  0°  ? 

9.  Three  liters  of  gas  are  measured  off  at  15°  and  76.7cm  barometric 
pressure.  Find  the  volume  of  this  gas  at  the  standard  temperature,  0°, 
and  at  the  standard  pressure,  76cm. 

10.   From  the  following  data  find  the  specific  heat  of  nickel : 
Weight  of  nickel  =  400s. 

"       "  water  =  200s. 

"  calorimeter  =  100s. 

Specific  heat  of  calorimeter  =0.1. 

Temperature  of  nickel  just  before  entering  water  =  100°. 
"  "  water    "        "      nickel  enters     =  15°. 

"the  whole  after        "         "         =  29°.  7. 

11.    From  the  following  data  find  the  temperature  after  mixing  water 
and  mercury : 

Weight  of  mercury  =  1000s. 

"       "  water  =  100s. 

Temperature  of  mercury  =  100°. 

"   water  =  10°. 

Specific  heat  of  mercury  =  0.0333. 

Number  of  units  of  heat  absorbed  by  the  calorimeter  =  80. 

12.  If  the  weight  of  a  mass  of  liquid  is  8s,  its  temperature  80°,  and  its 
specific  heat  0.24,  how  many  grams  of  a  second  liquid,  whose  temperature 
is  10°  and  specific  heat  0.48,  must  be  mixed  with  the  first  in  order  that 
the  resulting  temperature  may  be  50°  ? 

13.  How  many  grams  of  a  liquid  whose  temperature  is  70°  and  whose 
specific  heat  is  0.25  must  be  poured  on  20s  of  ice  at  0°  in  order  to  melt 
it  ?    The  latent  heat  of  melting  is  80. 

14.  How  many  grams  of  steam  at  100°  will  be  required  just  to  melt 
100s  of  ice  at  0°,  if  the  latent  heat  of  vaporization  is  537,  and  the  latent 
heat  of  melting  is  80  ? 

15.  What  temperature  on  the  Centigrade  scale  corresponds  to  —  27° 
on  the  Fahrenheit  ? 


CHAPTER   III. 
ELASTICITY. 

57.  Correction  of  the  Beading*  of  a  Spring1  Balance 
when  used  in  the  Horizontal  Position.  In  the  present 
chapter  the  student  will  find  a  series  of  experiments  on 
elasticity.  Some  knowledge  of  elasticity  will  prove  help- 
ful to  him  when  he  takes  up  the  study  of  sound  in  the 
next  chapter.  As  frequent  use  will  be  made  of  spring 
balances  in  our  work,  it  will  be  well  to  consider  the 
corrections  that  must  be  applied  to  their  readings. 

The  maker  of  a  spring  balance  intends  to  get  the  weight 
of  the  balance  hook  and  the  rod  that  connects  the  hook  to 
the  end  of  the  spiral  spring,  which  lies  within  the  balance 
frame,  so  adjusted  that,  when  the  balance  is  hung  up  by 
its  ring  with  no  weight  suspended  from  the  hook,  the 
pointer  will  be  just  opposite  the  zero  line.  Whenever  a 
balance  thus  suspended  has  its  pointer  not  opposite  the 
zero  line,  the  zero  error  is  found  by  observing  how  far  the 
pointer  is  above  or  below  this  line,  as  has  already  been 
mentioned  on  page  5. 

In  some  of  the  subsequent  experiments,  however,  we 
shall  have  occasion  to  use  the  spring  balance  held  not 
in  a  vertical  position,  as  was  intended  by  the  maker, 
but  in  a  horizontal  position.  Whenever  a  spring  balance 
with  nothing  hung  on  its  hook  is  held  in  a  horizontal 
position,  the  hook  and  the  connecting  rod  no  longer  pull 
on  the  spring,  so  the  spring  contracts  and  draws  the 


134  EXPERIMENTAL   PHYSICS. 

pointer  beyond  the  zero  line  until  the  pointer  strikes 
against  the  end  of  the  slot  in  which  it  moves,  or,  what 
amounts  to  the  same  thing,  until  a  projection,  near  which 
the  hook  is  fastened,  in  the  connecting  rod  comes  in  con- 
tact with  the  balance  frame.  If  we  should  lay  the  balance 
upon  a  table  with  its  ring  round  an  upright  rod  fastened  in 
the  table-top,  and  then  pull  in  a  horizontal  direction  on  the 
hook,  the  number  of  pounds'  or  grams'  pull,  as  registered 
by  the  pointer,  would  be  too  small  by  the  weight 
of  the  hook  and  connecting  rod ;  by  adding,  how- 
ever, this  weight  to  the  amount  registered  by  the 
pointer,  we  should  get  the  number  of  pounds  that 
we  are  really  pulling  on  the  hook.  The  purpose 
of  the  next  experiment  is  to  find  this  correction, 
that  is,  the  weight  of  the  hook  and  connecting  rod. 

Experiment  58.  To  find  the  correction  that 
must  be  applied  to  the  reading  of  a  given  spring 
balance  when  the  pull  upon  it  is  to  be  in  a  horizon- 
tal direction. 

Apparatus.  Two  30-pound  spring  balances;  two 
8-ounce  spring  balances. 

Directions.     Suspend  by  its  ring  one  of  the 
30-pound  spring  balances  so  that  it  shall  hang 
freely ;  then  hang  by  its  hook  the  other  30-pound 
spring  balance  (see  Fig.  40),  the  correction  of 
^^      which  is  to  be  found,  to  the  hook  of  the  spring 
FIG.  4o.    i3aiance  already  suspended.     Record  the  reading 
of  the  upper  spring  balance.     This  reading  is  the  weight 
of  the  lower  spring  balance.     Record  also  the  reading  of 
the  lower  spring  balance.      This  reading  is  the  weight 


ELASTICITY.  135 

of  all  of  the  lower  spring  balance  except  its  hook  and 
connecting  rod. 

What  is  the  weight  of  the  hook  and  connecting  rod  of 
the  lower  spring  balance  ? 

Repeat  the  experiment,  using  the  pair  of  8-ounce  spring 
balances  in  place  of  the  30-pound  spring  balances. 

In  this  case,  what  is  the  weight  of  the  hook  and  con- 
necting rod? 

EXAMPLES. 

1.  From  a  spring  balance  which  is  suspended  by  its  ring  another 
spring  balance  is  hung  in  an  inverted  position  by  its  hook.     If  the  spring 
balance  suspended  by  its  ring  reads  3. 7  oz. ,  and  the  other  spring  balance 
reads  3  oz.,  what  correction  must  be  applied  to  the  spring  balance  now 
reading  3  oz. ,  when  it  is  used  in  the  horizontal  position  ? 

2.  The   spring  balance,    the    correction    for   which   was   found  in 
Example  1,  is  used  in  the  horizontal  position.     The  spring  balance  reads 
5.3  oz.,  what  is  the  true  reading  ? 

3.  If    the  readings  of    two   spring  balances  are    the    same  as    in 
Example  1,  but  the  zero  error  of  the  spring  balance  which  is  being  tested 
is  0.2  oz.  (that  is,  the  spring  balance  when  suspended  by  its  ring  reads 
0.2  oz.  above  the  zero  line),  what  would  be  the  correction  for  the  spring 
balance  when  used  in  the  horizontal  position  ? 

Solution.  If  the  spring  balance  reads  3.0  oz. ,  its  reading  corrected  for 
the  zero  error  would  be  3.2  oz.,  so  the  weight  of  its  hook  and  rod  would 
be  3.7  —  3.2  =  0.5  oz.  Hence  0.5  oz.  must  be  added  to  the  reading  of 
the  spring  balance,  when  used  in  the  horizontal  position. 

4.  If  —0.3  oz.  is  the  zero  error  of  a  spring  balance  (that  is,  the  spring 
balance  when  suspended  by  its  ring  reads  0.3  oz.  below  the  zero  line),  and 
this  spring  balance  reads  3.9  oz.,  when  suspended  by  its  hook  from  the 
hook  of  another  spring  balance  which  reads  4  oz.,  what  correction  must 
be  applied  when  the  balance  is  used  in  the  horizontal  position  ? 

5.  A  spring  balance  the  zero  error  of  which  is  0.4  Ib.  is  suspended  by 
its  ring,  and  from  its  hook  is  hung  in  an  inverted  position  another  spring 
balance  the  zero  error  of  which  is  —0.3  Ib.     If  the  reading  of  the  spring 
balance  suspended  by  its  ring  is  3.2  Ibs.,  and  that  of  the  other  3.0  Ibs., 
what  correction  must  be  applied  to  the  reading  of  the  spring  balance 
which  has  been  thus  tested,  when  used  in  the  horizontal  position? 


136 


EXPERIMENTAL   PHYSICS. 


FORCE. 

58.  Meaning-  of  the  Term  Force.  The  term  force  is 
important  in  physics,  and  it  will  be  our  object  in  the 
earlier  of  the  following  experiments  to  make  the  meaning 
of  this  term  clear. 


Experiment  59, 

a  wire. 


To  find  the  tension  necessary  to  break 


Apparatus.  A  30-pound  spring  balance  ;  5  pieces  of  No.  30 
B.  &  S.  spring  brass  wire,  each  about  lm  long ;  a  wooden  guard  to 
slip  on  hook  of  the  balance. 

NOTE.  No.  30  B.  &  S.  means  that  the  size  of  the  wire  is  number  30, 
measured  on  the  Brown  and  Sharpe  wire-gauge. 

Directions.  Round  some  vertical  cylindrical  object 
like  a  gas-pipe  make  several  turns  with  one  en'd  of  one  of 
the  pieces  of  wire,  and  to  prevent  slipping 
fasten  this  end  to  a  tack  driven  into  the  wood- 
work to  which  the  pipe  is  fastened.  Pass  the 
other  end  through  the  eye  where  the  hook  is 
attached  to  the  balance,  and  fasten  by  twist- 
ing the  wire  about  itself.  Over  the  hook  slip 
the  wooden  guard,  and  wind  the  wire  round 
it  several  times,  as  shown  in  Fig.  41,  taking 
care  there  is  no  slack  wire  between  the  hook 
and  the  guard.  See  that  there  are  no  kinks  in 
Holding  the  balance  in  a  horizontal  position,  and 
taking  care  that  the  rod  of  the  balance  to  which  the  hook 
is  attached  does  not  bind  or  rub  against  the  frame  of  the 
balance,  gradually  increase  the  tension,  and  constantly 
watch  the  pointer  until  the  wire  breaks.  When  holding 


FIG.  41. 

the  wire, 


FOECE.  137 

the  balance,  avoid  having  the  hand  near  the  end  to  which 
the  hook  is  attached,  lest  the  finger  be  injured  by  the  recoil. 

Record  the  error  of  the  balance  when  used  in  the 
horizontal  position.  Also  record  the  number  of  pounds 
the  balance  indicates  when  the  wire  breaks. 

Why  were  you  directed  to  keep  the  wire  free  from 
kinks,  and  to  wrap  it  round  cylindrical  objects  like  the 
gas-pipe  and  the  wooden  guard? 

Using  a  new  piece  of  wire  each  time,  make  in  all  five 
tests.  Record  the  result  of  each  trial,  and  find  the 
average,  corrected  for  the  error  of  the  balance. 

The  tension,  or  pull,  required  to  break  the  wire  is 
called  the  breaking  strength  of  the  wire. 

Find  the  product  -of  453.6,  and  the  number  that 
expresses  the  average  breaking  strength.  This  product 
will  be  the  number  that  expresses  the  average  breaking 
strength  in  grams,  as  in  1  Ib.  there  are  453. 6g. 

Experiment  6O.  To  find  how  long  a  wire  must  be  to 
break  under  its  own  weight,  if  suspended  by  one  end. 

Apparatus.  A  horn-pan  balance  ;  lm  of  No.  30  B.  &  S.  spring 
1  >rass  wire  ;  a  micrometer  gauge. 

Directions.  Measure  off  accurately  lm  of  the  wire. 
Weigh  it  to  O.lg  on  the  horn-pan  balance. 

If  the  lm  of  wire  were  suspended  by  one  end,  how  hard 
\vould  it  pull  down  at  the  point  of  support  ? 

Turn  back  to  the  last  experiment,  and  get  the  record 
of  the  breaking  strength  of  the  wire  in  grams. 

Knowing  the  weight  of  lm  of  the  wire  and  its  breaking 
strength,  find  by  computation  the  length  of  a  piece  that 
would  break  of  its  own  weight,  if  supported  at  one  end. 


138  EXPERIMENTAL    PHYSICS. 

With  the  micrometer  gauge  measure  the  diameter  of  the 
wire ;  and  find  area  of  cross-section  of  wire,  using  formula 
A  =  ^TrD2.  Knowing  that  the  strength  of  wires  of  the 
same  material  as  well  as  their  weight,  for  equal  lengths, 
is  proportional  to  their  area  of  cross-section,  find  by  com- 
putation the  breaking  strength  of  a  brass  wire  lsqcm  in 
area  of  cross-section. 

ELASTICITY   OF   STRETCHING. 

Experiment  61.  To  find  whether  a  wire  will  increase 
by  equal  amounts  in  length  for  equal  additions  to  the  tension 
by  which  it  is  stretched. 

Apparatua  About  4m  of  No.  27  B.  &  S.  spring  brass  wire  ; 
a  30-pound  spring  balance;  two  meter  sticks  graduated  in  milli- 
meters ;  a  wooden  screw  and  nut ;  an  iron  screw ;  two  narrow 
mirrors. 

NOTE.  The  wooden  screw  and  nut  can  be  readily  obtained  from  a 
wooden  clamp  such  as  carpenters  use.  An  inspection  of  Fig.  42  will 
show  how  the  screw  and  nut  are  arranged.  The  side  of  the  clamp  next 
the  handle  of  the  screw  has  a  slot  cut  in  it  to  fit  the  edge  of  the  table. 
The  nut  is  made  by  sawing  off  a  piece  of  the  side  containing  the  thread 
in  which  the  screw  works,  and  should  have  a  strong  hook  fastened  to  it. 

Directions.  Into  the  top  of  a  table,  near  one  end, 
insert  the  iron  screw ;  and  solder  one  end  of  the  wire  to  it. 
By  passing  the  other  end  of  the  wire  through  the  eye  in 
which  the  balance  hook  is  fastened,  and  twisting  this  end 
round  the  wire,  make  it  fast.  Wind  the  wire  round  the 
hook  of  the  balance  several  times. 

Put  the  wooden  screw  and  nut  at  the  end  of  the  table 
remote  from  the  iron  screw.  Put  the  ring  of  the  balance 
over  the  hook  on  the  nut,  and,  by  turning  the  screw,  make 
the  balance  indicate  a  tension  of  1  Ib.  This  tension  will 


ELASTICITY    OF    STRETCHING.  139 

draw  the  wire  straight.  Now  solder1  two  pieces  of  fine  wire, 
each  about  0.5cm  in  length,  across  the  long  wire  at  right 
angles,  one  near  each  end,  to  serve  as  markers.  As  shown 
in  Fig.  42,  lay  a  meter  stick  lengthwise  under  each  end 
of  the  wire.  Lay  on  each  of  the  meter  sticks  a  narrow 
mirror,  and  adjust  each  meter  stick,  by  sliding  it  back 
and  forth,  till  the  marker  under  which  it  lies  is  exactly 


FIG.  42. 

over  one  of  the  divisions  of  the  meter  stick,  when  the 
eye  is  held,  as  it  should  always  be  held  in  making  read- 
ings in  this  experiment,  so  that  the  marker  obscures  its 
own  image.  Do  not  allow  the  meter  sticks  to  be  moved 
during  the  experiment. 

By  turning  the  screw  increase  the  tension  by  2  Ibs. 
(The  balance  now  reads  3  Ibs.)  Read  the  position  of  each 

1  In  order  to  solder  two  pieces  of  brass,  brighten  the  parts  to  be  joined 
by  careful  rubbing  with  a  file  or  with  emery  cloth.  Moisten  these  bright 
parts  with  soldering-fluid,  and  over  each  of  them  pass  the  tip  of  a  hot 
soldering-iron  on  which  is  a  drop  of  melted  solder  to  "tin"  or  coat  the 
surfaces.  Lay  the  tinned  surfaces  together,  moisten  them  with  soldering- 
fluid,  and  press  upon  them  the  hot  soldering-iron,  from  the  tip  of  which 
a  drop  of  solder  is  allowed  to  flow  and  to  spread  round  and  between 
the  surfaces.  Remove  the  soldering-iron,  and  let  the  solder  harden  at 
the  juncture.  Do  not  heat  the  soldering-iron  after  a  greenish  flame 
begins  to  play  round  it,  lest  the  tinning  at  its  tip  be  destroyed. 


140 


EXPERIMENTAL    PHYSICS. 


marker  to  quarters  of  a  millimeter ;  the  difference  between 
their  movements  is  the  amount  the  portion  of  the  wire 
lying  between  them  has  stretched.  Reduce  the  tension  to 

1  lb.,  and  notice  whether  the  wire  regains  its  original  length. 

Make  several  trials  similar  to  this,  increasing  the  force 

2  Ibs.  at  a  time  (making  the  balance  read  in  addition  to 
the  1  lb.,  which  is  always  kept  applied,  4  Ibs.,  and  then 
6  Ibs.)  until  the  wire  fails  to  return  to  its  original  length, 
when  the  tension  acting  on  the  wire  is  reduced  to  1  lb. 

In  recording  the  results,  do  not  count  the  force  of  1  lb. 
applied  to  keep  the  wire  straight. 

The  results  may  be  recorded  as  follows : 


MATERIAL,  OF  WIRE 


GAUGE  No.  ..  LENGTH  ... 


TENSION.. 

MOVEMENT  OF 
FIRST  MARKER. 

MOVEMENT  OF 
SECOND  MARKER. 

ELONGATION. 

ELONGATION 
PER  POUND. 

lb. 

ram. 

mm. 

mm. 

mm. 

Measure  and  record  in  millimeters  the  length  of  the 
wire  between  the  two  markers. 

For  what  value  of  the  tension  does  the  wire  fail  to 
return  to  its  original  length,  after  the  pull  on  the  wire 
has  been  reduced  to  1  lb.  ? 

Does  the  amount  of  elongation  show  any  simple  relation 
to  the  amount  of  tension  ? 

(HINT.  In  answering  this  question,  look  at  the  first  column  and  at 
the  fourth  of  your  record.) 


ELASTICITY   OF   STRETCHING.  141 

The  answer  to  the  last  question,  which  should  be 
modelled  after  the  statement  of  Laws  2  and  3  below,  con- 
stitutes what  we  shall  call  Law  1  for  the  stretching  of  a 
wire. 

Law  2.  For  a  given  tension,  elongation  is  proportional 
to  the  length  of  the  wire  ;  that  is,  the  longer  the  wire,  the 
greater  the  elongation. 

Law  3.  For  a  given  tension,  the  elongation  is  inversely 
proportional  to  the  area  of  cross-section  of  the  wire ;  that 
is,  the  larger  the  area  of  the  cross-section  of  the  wire,  the 
less  the  elongation. 

How  could  you  prove  experimentally  Law  2  ?     Law  3  ? 

In  Exp.  59  the  tension  was  so  great  that  the  wire 
broke,  while  in  the  present  experiment  the  tension  simply 
stretched  the  wire.  A  tension  or  pull  is  called  a  force. 
In  Exp.  28  the  air  confined  in  the  closed  branch  of  the 
Boyle's  tube  was  compressed  or  pushed  into  a  smaller 
volume  by  the  weight  of  the  mercury.  This  compressing 
action  or  push  is  also  called  a  force. 

Definition.     A  force  is  a  push  or  a  pull. 

The  power  which  a  body  has  of  recovering,  more  or  less 
completely,  its  original  shape  after  the  force  which  has 
changed  the  shape  is  withdrawn,  is  called  elasticity  of 
shape  or  figure. 

Tf  stretched  or  compressed  within  certain  small  limits 
(that  is,  stretched  or  compressed  only  a  little),  most  solid 
bodies  will  return  to  their  original  dimensions,  after  the 
forces,  to  which  they  have  been  exposed,  cease  to  act. 
These  limits  are  called  the  limits  of  elasticity. 

In  this  experiment,  did  you  stretch  the  wire  beyond  its 
limits  of  elasticity? 


142  EXPERIMENTAL    PHYSICS. 


ELASTICITY   OF   BENDING. 

59.  Effects  of  Bending1.  In  the  preceding  experiment 
we  observed  that  a  wire  had  the  power  of  recovering  its 
original  length  more  or  less  completely  when  the  force 
which  stretched  it  ceased  to  act.  In  the  next  four  experi- 
ments we  shall  continue  our  work  in  elasticity  by  study- 
ing the  effects  produced  by  bending  rods  of  different 
dimensions. 

Experiment  62.  To  find  the  relation  between  the  load 
and  the  amount^  of  lending  produced  in  a  rod  supported  at 
each  end. 

Apparatus.  A  straight  rod  of  clear  white  pine  a  little  more  than 
100cm  long,  and  about  lcm  wide,  and  lcm  thick;  three  triangular 
prisms  of  wood  ;  weights  from  100^  to  4008 ;  a  scale  about  10cm  long 
with  a  support  to  keep  it  in  a  vertical  position  ;  a  very  light,  thin 
rod  of  wood  about  32cm  long,  called  a  pointer  ;  a  meter  stick. 

Directions.  Lay  the  rod  in  a  horizontal  position  on 
two  of  the  triangular  blocks,  placed  parallel  to  each  other 
with  their  centers  lm  apart.  The  rod  should  be  parallel 
to  the  edge  of  the  table  and  a  little  more  than  30cm  from 
the  edge.  Place  the  remaining  block  opposite  the  middle 
of  the  rod  and  parallel  to  it.  The  center  of  this  block  is 
to  be  5cm  from  the  nearer  edge  of  the  rod,  as  shown  in 
Fig.  43.  By  placing  one  end  under  the  center  of  the  rod, 
support  the  pointer  on  the  block,  so  that  it  lies  across  the 
block,  and  at  right  angles  to  the  rod.  Place  with  its  back 
turned  towards  the  rod,  in  a  vertical  position,  the  10cm 
scale  at  a  distance  of  30cm  from  the  edge  of  the  rod,  and 
close  beside  the  pointer.  The  movement  of  the  end  of 


ELASTICITY    OF    BENDING.  143 

the  pointer  will  magnify  the  bending  of  the  rod  five 
times.  The  support  on  which  the  pointer  rests  should 
be  a  little  higher  than  the  supports  of  the  rod,  so  that 
the  pointer  will  rest  against  the  front  edge  of  the  rod 
throughout  the  experiment,  and  so  continue  to  magnify 
the  bending  of  the  rod  five  times. 

Sight  carefully  across  the  upper  surface  of  the  pointer, 
and  record  its  position  on  the  10cm  scale.  Then  on  the 
middle  of  the  rod  lay  carefully  a  100g  weight,  and  again 


FIG.  43. 


read  the  position  of  the  pointer.  (If  the  weights  are  not 
flat,  lay  the  weights  in  a  little  pan,  as  shown  in  Fig.  43.) 
Remove  this  weight,  and  read  and  record  again  the  posi- 
tion of  the  pointer.  The  weight  applied  to  the  rod  is 
called  the  load.  Now  put  on  20 Og,  and  read  and  record 
the  position  of  the  pointer.  Also  take  the  reading  of  the 
pointer  with  the  load  off.  Then  add  300g  and  400g  in 
turn,  reading  and  recording  the  position  of  the  pointer 
every  time  the  load  is  put  on,  and  also  when  it  is  taken  off, 


144 


EXPERIMENTAL    PHYSICS. 


If  permanent  bending  should  be  observed,  stop  recording 
the  readings. 

When  weights  are  put  on  and  taken  off,  see  that  the 
rod  is  not  shifted  on  its  supports. 

The  following  form  for  recording  observations  is  sug- 
gested : 


SUPPORTS  100cm  APART.      WIDTH  OF  ROD 


THICKNESS  OF  ROD 


LOAD. 

READING 

WITH 

READING 

WITHOUT 

AVERAGE 
READING 

RISE 
OF  POINTER 

DEFLEC- 
TION 

DEFLEC- 
TION 

LOAD. 

LOAD. 

WITHOUT 

ON  SCALE. 

OF  ROD. 

PER    lOOg. 

LOAD. 

g- 

cm. 

cm. 

era. 

cm. 

cm. 

cm. 

3.00 

100 

3.40 

3.00 

0.40  -f-  5 

=  0.080 

0.080 

3.00 

200 

3.75 

2.98 

0.77  -r  5 

=  0.154 

0.077 

2.96 

Find  the  average  of  the  numbers  in  the  column  headed 
"Deflection  per  100g." 

Divide  each  load  in  the  first  column  of  your  observa- 
tions by  the  first  load  (100g) ;  also  divide  each  deflection 
in  the  sixth  column  by  the  first  deflection  (the  deflection 
produced  by  a  load  of  100g). 

From  the  results  thus  obtained,  what  should  you  say  is 
the  relation  between  the  load  and  the  bending  produced  ? 

QUESTION.  If  a  load  of  100s  produces  a  bending  of  0.25cm,  what  will 
be  the  amount  of  bending  produced  by  a  load  of  300s  ? 

NOTE.  Sometimes  the  load  is  referred  to  as  the  transverse  force.  The 
expressions  amount  of  bending  and  amount  of  flexure  have  the  same 
meaning,  signifying  the  distance  through  which  the  middle  of  the  rod  is 
depressed. 


ELASTICITY    OF    BENDING.  145 

Experiment  63.  To  find  the  relation  between  the  length 
of  rods  and  the  amount  of  bending  produced  by  equal  loads. 

Apparatus.  The  same  as  in  the  last  experiment ;  weights  from 
500s  to  20008. 

Directions.  Arrange  the  apparatus  in  all  respects  as 
in  the  last  experiment,  with  the  exception  of  having  the 
supports  placed  at  a  distance  of  50cm  instead  of  100cm 
apart.  Let  the  middle  portion  of  the  rod  be  subjected  to 
the  bending,  that  is,  let  about  25cm  of  each  end  of  the  rod 
project  over  each  support. 

Using  the  same  precautions  as  already  mentioned  for 
the  preceding  experiment,  and  adding  500g  at  a  time, 
load  from  500g  to  2000g.  Record  as  before,  and  find  the 
average  of  the  deflections  per  100g. 

Divide  the  average  of  the  deflections  per  100g  of  the 
last  experiment  by  the  corresponding  average  of  the 
present  experiment ;  also  divide  the  length  (the  distance 
between  the  supports)  of  the  longer  rod  by  that  of  the 
shorter. 

If  the  quotients  thus  obtained  are  not  equal,  try  to 
make  them  equal  by  squaring  or  cubing  one  of  them. 

What  relation  should  you  say  exists  between  the  length 
of  rods  and  their  amount  of  flexure  ? 

QUESTION.  If  a  rod  100cm  long,  when  loaded  with  100s,  is  bent  0.12cm, 
how  much  will  the  same  load  bend  a  rod  50cm  long  ? 

Experiment  64.  To  find  the  relation  between  the  breadth 
of  rods  and  the  amount  of  bending  produced  by  equal  loads. 

Apparatus.  With  the  exception  of  the  rod  and  weights,  the  same 
as  in  the  last  experiment ;  a  straight  rod  of  clear  white  pine  a  little 
more  than  100cm  long,  and  about  lcm  thick  and  2cm  wide  ;  weights 
from  2008  to  8008. 


146  EXPERIMENTAL   PHYSICS. 

Directions.  Lay  the  rod  on  its  broad  side  with  the 
supports  100cm  apart.  Adding  200g  at  a  time,  load  from 
200g  to  800g.  Record  as  before. 

In  this  experiment  and  in  Exp.  62  we  have  rods  alike 
in  all  respects  except  that  of  width.  Divide  the  average 
deflection  per  100g  of  the  rod  of  Exp.  62  by  the  corre- 
sponding average  for  the  rod  of  this  experiment  ;  also 
divide  the  width  of  the  rod  of  the  present  experiment 
by  the  width  of  the  rod  used  in  Exp.  62. 

Are  the  two  quotients  equal  or  nearly  equal  ? 

What  relation  can  you  make  out  as  probably  existing 
between  the  breadth  of  rods  and  the  amount  of  flexure  for 
equal  loads  ? 

QUESTION.  If  a  rod  lcm  wide  is  bent  0.12cm  by  a  load  of  100s,  how 
much  will  the  same  load  bend  a  rod,  of  equal  length  and  thickness,  and 
2c 


Experiment  65.  To  find  the  relation  between  the  thick- 
ness (depth)  of  rods  and  the  amount  of  bending  produced  by 
equal  loads. 

Apparatus.  With  the  exception  of  the  weights,  the  same  as  in  the 
preceding  experiment  ;  weights  from  500s  to  200(K 

Directions.  Use  the  broad  rod  of  the  preceding  experi- 
ment. Place  this  rod  on  edge  with  the  supports  100C1U 
apart.  Adding  500g  at  a  time,  load  from  500g  to  2000g. 
Record  as  before. 

This  rod  is  of  the  same  dimensions  as  that  used  in 
Exp.  62,  with  the  exception  of  that  of  thickness  (depth). 
Divide  the  average  deflection  per  100g  of  the  rod  of  Exp. 
62  by  the  corresponding  average  of  the  rod  of  this 
experiment;  also  divide  the  thickness  of  the  rod  of  this 
experiment  by  that  of  the  rod  used  in  Exp.  62. 


ELASTICITY   OF    TORSION.  147 

If  the  two  quotients  are  not  equal,  try  to  make  them 
equal  by  squaring  or  cubing  one  of  them. 

What  relation  can  you  make  out  as  probably  existing 
between  the  thickness  of  rods  and  the  amount  of  bending 
for  equal  loads  ? 

In  the  experiments  on  bending,  have  you  tested  the 
strength  or  the  stiffness  of  the  rods  ?  • 

QUESTION.  If  a  load  of  100s  bends  a  rod  lcm  thick  0.12cin,  how  much 
will  the  same  load  bend  a  rod  2cm  thick  ? 


ELASTICITY    OP    TORSION. 

6O.  Effects  of  Twisting-.  The  elasticity  of  torsion,  or 
twisting,  is  shown  by  the  alternate  twisting  and  untwisting 
when  a  weight  is  suspended  from  an  ordinary  string. 

Experiment  66.  To  find  the  relation  between  the  amount 
of  twisting  of  a  rod  and  the  force  applied. 

Apparatus.  A  rod  of  clear  ash  about  lm  long  and  £  by  £  in.  in 
cross-section  ;  one  end  of  this  rod  is  fitted  into  the  middle  of  a  circular 
board  1  ft.  in  diameter ;  a  sheet  of  cardboard  upon  which  is  traced 
a  circle  whose  diameter  is  somewhat  greater  'than  that  of  the  circular 
board,  and  whose  circumference  is  divided  into  degrees  ;  two  8-ounce 
spring  balances  ;  a  narrow  mirror  to  be  used  as  in  Exp.  61. 

Directions.  Upon  a  table,  having  uprights  at  each  end 
which  support  a  movable  cross-piece,  place  the  cardboard 
with  the  graduated  circle  uppermost,  with  the  hole  in  its 
center  over  the  hole  in  a  metallic  plate  set  into  the  table- 
top  under  the  cross-piece.  Place  the  rod  upright  with 
the  stout  pin,  which  projects  from  the  center  of  the  board, 
in  the  hole  in  the  table-top.  Fasten  by  a  clamp,  as  shown 


148 


EXPEKIMENTAL    PHYSICS. 


in  Fig.  44,  the  other  end  of  the  rod  in  the  long  slot  in  the 
movable  cross-piece  above  the  table.  The  length  of  the 
rod  from  the  top  of  the  circular  board  to  the  cross-piece 
must  be  80cm.  To  get  the  right  length,  adjust  the  cross- 
piece.  Do  not  let  the  circular  board  rub  on  the  cardboard ; 


FIG.  44. 

do  not  let  the  peg  bind  in  the  hole.  By  means  of  tacks, 
fasten  the  cardboard  at  the  corners  to  the  table.  The 
circle  on  the  cardboard  and  circular  board  must  be  con- 
centric. Have  the  zero  mark  on  the  circle  just  beneath  a 
pin  driven  into  the  edge  of  the  circular  board  for  an  index. 
To  each  of  the  screws  inserted,  from  diametrically  oppo- 
site points,  into  the  edge  of  the  circular  board,  attach  a 


ELASTICITY   OF   TO] 


piece  of  flexible  string.  To  each  string  attach  an  8-ounce 
spring  balance,  and  with  these  balances  pull  horizontally 
in  opposite  directions  at  right  angles  to  the  line  joining 
the  screws.  Let  the  force  be  the  same  for  each  balance, 
and,  as  the  rod  twists,  let  the  direction  of  the  pull  be 
changed  in  such  a  way  as  to  keep  it  always  at  right  angles 
to  the  line  joining  the  screws.  Use  in  succession  forces  of 
2, 4,  6,  and  8  oz.,  and  record  in  each  case  the  resulting  tor- 
sion (that  is,  the  number  of  degrees)  as  shown  by  the  read- 
ings on  the  cardboard  scale.  Of  course,  as  shown  in 
Exp.  58,  a  correction  must  be  added  to  the  indication  of 
the  spring  balance,  when  used  in  the  horizontal  position, 
to  get  the  true  measure  of  the  force  ;  so  this  correction  for 
each  spring  balance  must  be  found  and  recorded. 
The  following  form  of  record  is  suggested : 

ROD  or  CROSS-SECTION  £  BY  £  IN.;   LENGTH  80cm. 


AVERAGE 

TWISTING 
FORCE. 

READING 

WITH 

TWISTING 
FORCE. 

READING 

WITHOUT 

TWISTING 
FORCE. 

READINGS 

WITHOUT 

TWISTING 
FORCE. 

TWIST  OF 
ROD. 

TWIST  OF 
ROD  PER 
1  oz. 

oz. 

o 

0 

0 

o 

0 

1 

2 

3 

1 

2 

1 

1 

4 

5 

1 

4 

1 

1 

Divide  each  twisting  force  in  the  first  column  of  your 
record  by  the  first  twisting  force  (2  oz.) ;  also  divide  each 
twist  of  rod  in  the  fifth  column  by  the  first  twist  (pro- 
duced by  the  twisting  force  of  2  oz.). 


150  EXPERIMENTAL   PHYSICS. 

From  the  results  thus  obtained,  what  should  you  say  is 
the  relation  between  the  force  applied  and  the  twisting 
produced  ? 

QUESTION.  If  a  force  of  5  oz.  twists  a  certain  rod  1.5°,  through  how 
many  degrees  will  a  force  of  12  oz.  twist  the  rod  ? 

Experiment  67.  To  find  the  relation  between  the  amount 
of  twisting  for  equal  forces  and  the  lengths  of  rods. 

Apparatus.  The  same  as  in  the  preceding  experiment,  but  instead 
of  the  two  8-ounce  spring  balances,  two  4-pound  spring  balances. 

Directions.  Arrange  everything  as  in  the  preceding 
experiment,  but  lower  the  cross-piece  so  that  only  40cm  of 
the  length  of  the  rod  shall  be  subject  to  torsion.  Find 
and  record  the  corrections  for  the  spring  balances,  and, 
using  forces  of  4,  8,  16,  and  32  oz.,  proceed  as  before  and 
record  the  results. 

Turn  back  to  Exp.  66  to  find  the  average  twist  of  rod 
per  ounce.  Divide  this  twist  by  the  corresponding  aver- 
age twist  of  the  rod  of  the  present  experiment.  Divide 
the  length  of  the  rod  of  Exp.  66  by  that  of  the  rod  of  the 
present  experiment. 

Are  the  quotients  equal  or  nearly  equal  ? 

Can  you  state  a  probable  relation  between  the  twisting 
for  equal  forces  and  the  length  of  rods  ? 

QUESTION.  If  a  force  of  8  oz.  twists  a  rod  100cm  long  3°,  through 
how  many  degrees  will  the  same  force  twist  a  rod  whose  length  is  50cm  ? 

Experiment  68.  To  find  the  relation  between  the  diam- 
eters of  the  cross-section  of  rods  and  the  amount  of  twisting 
produced  by  equal  forces. 

Apparatus.  The  same  as  in  the  preceding  experiment,  except 
that  a  rod  of  clear  ash  of  cross-section  f  by  £  in.  is  used. 


ELASTICITY    OF    TORSION.  151 

Directions.  Clamp  the  rod  so  that  a  length  of  80cm 
shall  be  subject  to  torsion.  Find  and  record  the  correc- 
tions for  the  spring  balances.  Apply  forces  of  1,  2,  3,  and 
4  Ibs.  (that  is,  16,  32,  48,  and  64  oz.).  Record  as  before. 

Divide  the  average  twist  per  ounce  of  the  rod  (whose 
diameter  is  i  in.)  of  Exp.  66  by  the  average  twist  of  the 
rod  (whose  diameter  is  f  in.)  of  the  present  experiment ; 
also  divide  the  diameter  of  the  rod  of  the  present  experi- 
ment by  that  of  Exp.  66. 

How  nearly  do  your  results  agree  with  the  statement, 
"  The  amount  of  torsion  is  inversely  proportional  to  the 
fourth  power  of  the  diameter  "  ? 

QUESTION.  If  a  rod  whose  diameter  is  1  in.  is  twisted  by  a  certain 
force  through  an  angle  of  5°,  through  how  many  degrees  would  the  same 
force  twist  a  similar  rod  whose  diameter  is  2  in.  ? 

61.  Elasticity  of  Volume.     Besides  elasticity  of  shape 
or  figure,  a  body  possesses  elasticity  of  volume,  or  the  power 
of  recovering,  more  or  less  perfectly,  its  original  volume 
after  the  force  which  has  changed  the  volume  is  withdrawn. 

Elasticity  of  volume  is  possessed  in  perfection  by  liquids 
and  gases,  which  recover  completely  their  original  volumes 
when  the  compressing  forces  are  removed,  no  matter  how 
long  they  have  been  applied.  In  Exp.  28  the  weight  of 
mercury  in  the  open  branch  compressed  the  air  in  the 
closed  branch,  thus  making  it  occupy  a  smaller  volume ; 
but  when  the  pressure  is  removed,  the  air,  by  reason  of  its 
elasticity  of  volume,  returns  to  its  former  bulk. 

62.  Strain ;    Stress ;   Hooke's  Law.     Any  change  in 
the  shape  or  size  of  a  body  is  called  a  strain.     Any  appli- 
cation of  force  tending  to  produce  a  strain  is  called  a  stress. 


152  EXPERIMENTAL   PHYSICS. 

In  Exp.  61  the  elongation  of  the  wire  is  a  strain,  and 
the  tension  that  produced  the  elongation  is  a  stress. 

In  the  experiments  on  bending  and  twisting,  the  stu- 
dent should  point  out  the  strain  and  the  stress. 

NOTE.  Many  years  ago  an  Englishman,  named  Hooke,  discovered 
Law  I.  of  stretching ;  hence  this  law  is  often  called  Hooke's  Law.  Hooke 
stated  his  law  in  the  following  words :  "  Ut  tensio  sic  vis." 

Using  the  words  stress  and  strain  as  just  denned,  could 
Hooke's  Law  be  stated  thus  ? 

"  The  stress  is  proportional  to  the  strain." 


EXAMPLES. 

Before  working  the  following  set  of  examples,  collect  into  a  group  the 
three  laws  of  stretching  (see  Exp.  61),  the  four  laws  of  bending  (see  Exps. 
62,  63, 64,  and  65),  and  the  three  laws  of  torsion  (see  Exps.  66,  67,  and  68). 

1.  A  balance,  the  zero  error  of  which  is  —  0.2  lb.,  weighs  1.7  Ib. 
When  this  balance  is  suspended  by  its  hook,  the  pointer  indicates  1.5  lb. 
What  correction  must  be  applied  to  the  reading  of  the  balance  when  it  is 
used  in  the  horizontal  position  ? 

2.  If  a  wire  3m-long  and  0.26<imm  in  area  of  cross-section  is  stretched 
2.5mm  by  a  force  of  2ke  (2000e),  how  great  a  force  would  be  required  to 
stretch  by  3mm  a  wire  of  like  material  12m  long  and  2s(i nim  in  area  of 
cross-section  ? 

Solution.  If  a  wire  3m  long  and  0.2s<imm  in  area  of  cross-section  is 
stretched  2.5mm  by  a  force  of  2k&,  a  force  of  lks  would  stretch  the  wire 

2  5 
one-half  as  much,  or  -irmm  (stretching  is  proportional  to  the  tension).,  and 

this  force  of  lks  would  stretch  a  length  of  lm  of  the  wire  one-third  as 
much,  or  ~;rmm  (stretching  is  proportional  to  the  length).  Finally,  if  the 
area  of  cross-section  of  the  wire  were  lsi mm,  a  length  of  lm  of  the  wire 
would  be  stretched  by  a  force  of  lks,  two-tenths  as  much,  or  ~  =  7^inm 
(stretching  is  inversely  proportional  to  the  area  of  the  cross-section). 


EXAMPLES.  153 

If  by  x  we  denote  the  force  required  to  stretch  the  second  wire  3mm, 
we  shall  find  by  a  process  precisely  like  the  one  just  given  that  a  wire  1™ 

long  and  isqmm  in  area  of  cross-section  will  be  stretched  — mm  by  a  force 

zx 

Of  1*8. 

As  the  material  is  the  same  for  each  wire,  we  have 

—  =  — 

2x~  12 

2x=  12 
.-.*==  6 

Hence,  theT  force  required  to  stretch  the  second  wire  will  be  6k*. 

3.  If  a  wire  8m  long  and  0.4s(imm  in  area  of  cross-section  is  stretched 
10mm  by  a  force  of  5k«,  how  great  a  force  would  be  required  to  stretch  by 
5mm  a  wire  of  like  material  20m  long  and  48(imm  in  area  of  cross-section  ? 

4.  If  a  wire  10m  long  and  lmm  in  diameter  is  stretched  10mm  by  a  force 
of  10ks,  ho'w  many  millimeters  would  a  force  of  8kg  stretch  a  wire  of  like 
material  25m  long  and  2mm  in  diameter  ? 

s  5.  What  is  the  ratio  of  the  stiffness  of  a  rod  60cm  long  to  that  of 
another  rod  I20cm  long,  but  of  the  same  width,  thickness,  and  material 
as  the  first  ? 

6.  If  a  rod  4  ft.  long,  2  in.  broad,  and  0.5  in.  thick  is  bent  0.1  in.  by  a 
weight  of  10  Ibs. ,  how  much  would  a  force  of  2  Ibs.  bend  a  rod  of  like 
material  12  ft.  long,  4  in.  broad,  and  2  in.  thick  ? 

Solution.  It  a  rod  4  ft.  long,  2  in.  broad,  and  0.5  in.  thick  is  bent  0.1 
by  a  weight  of  10  Ibs.,  a  weight  of  1  Ib.  would  bend  it  one-tenth  as  much, 

or  -^r  in.  (bending  is  proportional  to  the  load),  and  this  weight  of  1  Ib. 

would  bend  a  rod  1  ft.  long  only  one  sixty-fourth  as  much,  or  —  -  in. 

o40 

(bending  is  proportional  to  the  cube  of  the  Jength).     If  the  rod  were  1  ft. 
long  and  1  in.  wide,  the  weight  of  1  Ib.  would  bend  it  twice  as  much,  or 

0.2 

Trrr  in.  (bending  is  inversely  proportional  to  the  breadth).    Finally,  if  the 

u4U 

thickness  of  the  rod  were  1  in.,  its  length  1  ft.,  and  its  breadth  1  in.,  a 
force  of  1  Ib.  would  bend  it  one  hundred  and  twenty-five  thousandths  as 

much,  or  -^   '—  =  -£—  in.  (bending  is  inversely  proportional  to  the  cube  of 

u40 

the  thickness). 


154  EXPERIMENTAL   PHYSICS. 

If  by  x  we  denote  the  amount  the  second  rod  would  be  bent  by  a 
weight  of  2  Ibs.,  we  shall  find  by  a  process  precisely  like  the  one  just 

given  that  a  rod  1  ft.  long,  1  in.  broad,  and  1  in.  thick  will  be  bent  — - 

in.  by  a  force  of  1  Ib. 

As  the  material  is  the  same  for  each  rod,  we  have 
x         0.1 
108      2560 
2560  x  -  10.8 

.-.  x  =  0.0042 
Hence,  the  amount  the  second  rod  would  be  bent  is  0.0042  in. 

7.  If  a  rod  4m  long,  6cra  wide,  and  8cm  thick  is  depressed  0.75cm  at  its 
middle  point  by  a  certain  load,  how  much  would  the  same  load  depress  a 
rod  3m  long,  3cm  wide,  and  4cm  thick  ? 

8.  If  a  rod  100cm  long,  2«n  broad,  and  3cm  thick  is  deflected  0.5cm, 
what  would  be  the  deflection,  under  the  same  load,  of  a  rod  50cm  long, 
2cra  broad,  and  lcm  thick  ? 

9.  If  a  certain  beam  16  ft.  long,  4  in.  wide,  and  6  in.  thick  is  bent 
1  in.  by  a  load  of  500  Ibs.  placed  at  its  middle,  how  much  would  a  beam 
10  ft.  long,  8  in.  wide,  and  12  in.  thick  be  bent  by  the  same  load  ? 

10.  A  certain  beam  4  ft.  long  is  bent  downwards  0.5  in.  by  a  load 
placed  at  the  middle.     If  it  were  8  ft.  long,  how  far  would  it  be  bent  by 
the  same  load  ? 

11.  There  are  two  beams  of  the  same  length,  breadth,  and  material. 
One  beam,  which  is  8  in.  thick,  is  bent  1.6  in.  by  a  certain  load,  while  the 
other  beam  is  bent  0.2  in.  by  an  equal  load.     What  is  the  thickness  of 
the  second  beam  ? 

12.  If  a  rod  80cm  long  is  twisted  through  an  angle  of  1.5°  by  a  force 
of  4  oz.,  through  how  many  degrees  will  a  force  of  3  oz.  twist  a  rod 
100cm  long,  the  other  dimensions  as  well  as  the  material  being  the  same 
as  that  of  the  first  rod  ? 


CHAPTER    IV. 
SOUND. 

63.  Wave-Motion.  If  a  stone  is  dropped  into  a  pool 
of  calm  water,  the  stone  immediately  forces  down  and  dis- 
places a  number  of  particles  of  water;  consequently  the 
surrounding  particles  of  water  are  heaped  above  the  gen- 
eral level ;  these  descend  and  throw  up  another  wave,  and 
this  in  subsiding  raises  another,  until  the  force  of  the 
original  and  loftier  wave  dies  away  at  the  edge  of  the 
pool  in  the  faintest  ripples.  You  have  probably  noticed 
the  waves  that  spread  in  ever-widening  circles  over  a 
pool  when  the  water  has  been  disturbed  as  described. 
Did  you  ever  ask  yourself  the  question,  "  Do  the  particles 
of  water  forming  the  first  wave,  in  the  center  of  the  pool, 
pass  to  the  second  wave,  and  so  on  to  the  third,  and  finally 
reach  the  margin  of  the  pool  ?  "  This  question  is  easily 
answered  by  watching  the  movements  of  a  bit  of  wood 
floating  on  the  surface.  The  wood  simply  bobs  up  and 
down;  it  does  not  approach  the  shore.  Since  the  wood 
only  rises  and  falls,  we  see  that  the  particles  of  water  on 
which  it  rests  are  not  approaching  the  shore,  but  are  only 
moving  up  and  down.  Hence  it  is  not  the  particles  of 
water,  but  the  wave  form  that  travels  from  the  center  to 
the  margin  of  the  pool.  When  in  summer  a  wind  blows 
over  a  field  of  grain,  we  see  the  wave  form  advancing,  but 
we  know  that  the  ears  of  grain  are  simply  nodding. 


156  EXPERIMENTAL   PHYSICS. 

If  into  a  pool  of  water  we  drop  two  pebbles  at  a  little 
distance  apart,  we  shall  notice  that  two  sets  of  waves  are 
produced,  each  set  having  for  its  center  the  point  where 
the  pebble  entered  the  water.  As  the  waves  spread,  those 
of  one  set  cross  those  of  the  other.  If  we  look  carefully, 
we  shall  see  that  where  the  crest,  or  top,  of  one  wave 
coincides  with  the  crest  of  another,  an  elevation  higher 
than  the  crest  of  either  wave  is  produced;  also,  that 
where  the  trough,  or  hollow,  of  one  wave  coincides  with 
the  trough  of  another,  a  depression  deeper  than  the  trough 
of  either  is  formed;  finally,  if  two  waves  of  equal  size 
come  together  in  such  a  way  that  the  crest  of  one  coin- 
cides with  the  trough  of  the  other,  there  is  neither  an 
elevation  nor  a  depression,  but  a  calm. 

The  distance  from  crest  to  crest,  or  from  trough  to 
trough,  is  called  a  wave-length. 

Definition.  A  wave-length  is  the  distance  from  any  par- 
ticle to  the  next  particle  that  is  in  a  similar  position  in  its 
path,  and  is  moving  in  the  same  direction.  . 

In  Fig.  45  take  the  particle  a-,  b  is  in  the  same  posi- 
tion, but  when  a  is  moving  downwards  b  moves  upwards. 


FIG.  45. 


c  is  the  next  particle  in  the  same  position,  but  as  a  moves 
downwards  c  moves  downwards.  The  distance  from  a  to 
c  measured  in  a  straight  line  is  a  wave-length. 


THE    PENDULUM.  157 

Let  the  student,  by  dipping  his  finger  into  the  water 
contained  in  a  pail  and  then  quickly  removing  it,  set  up  a 
series  of  waves  as  has  already  been  described. 

After  the  waves  strike  the  sides  of  the  pail,  are  they 
sent  back  towards  the  center? 

By  using  a  finger  of  each  hand,  disturb  the  water  in 
such  a  way  as  to  produce  two  series  of  waves.  One  series 
mingles  with  the  other. 

Do  you  notice  any  phenomena  of  interference  (that  is, 
calms  and  places  of  greater  or  less  elevation  produced  by 
the  mingling  of  the  waves)  ? 

You  should  repeat  these  observations  till  the  eye  becomes 
trained  to  catch  the  modifications  of  the  wave  form. 


THE   PENDULUM. 

64.  The  Simple  Pendulum.  When  the  surface  of 
water  is  agitated,  the  particles  of  water  move  up  and 
down  with  a  rythmic  motion.  It  is  important  to  under- 
stand the  chief  laws  this  rythmic  motion  obeys.  The 
motion  of  the  pendulum  is  of  the  same  nature  as  that  of 
the  water  particles,  so  by  experimenting  with  the  pendu- 
lum, we  shall  get  some  knowledge  of  the  motion  of  the 
water  particles. 

The  pendulum  we  shall  use  will  consist  of  a  lead  bullet 
attached  to  a  firm  support  by  a  thread,  which  will  allow 
the  bullet  to  swing  freely.  The  bullet  is  called  the  bob  of 
the  pendulum.  The  fixed  point  to  which  the  thread  is 
attached  is  called  the  center  of  suspension  of  the  pendulum. 
A  motion  from  side  to  side  is  called  an  oscillation  ;  a  motion 
from  one  side  to  the  other  and  back  again  is  called  a  vibra- 


158  EXPERIMENTAL   PHYSICS. 

tion,  so  that  there  are  two  oscillations  in  one  vibration. 
The  distance  the  bob  swings  through,  in  going  from  its 
middle  position  to  its  extreme  position,  is  called  the  ampli- 
tude of  vibration.  The  distance  from  the  center  of  suspen- 
sion to  the  center  of  the  bob  is  called  the  length  of  the 
pendulum.  The  length  of  time 
a  pendulum  takes  to  make  an 
oscillation  is  called  the  time  of 
oscillation. 


Experiment    69.      To  find     /* 

whether  a  change  of  amplitude  £_ 

has  any  effect  upon  the  num- 
ber of  vibrations  per  minute  of  a  pendulum. 

Apparatus.  The  apparatus  used  is  shown  in  Fig.  46. 
A  spool  is  fastened  by  a  screw  near  the  edge  of  some  suitable 
support,  fastened  to  the  wall  a  little  more  than  7  ft.  above  the 
floor.  The  screw  is  "  set  up  "  till  it  turns  with  considerable 
friction.  A  silk  thread  about  3m  long  is  wound  round  the 
spool  and  made  to  pass  through  the  slot  in  the  head  of  the 
other  screw.  The  lower  end  of  the  thread  is  fastened  to  a 
bullet,  the  bob.  The  length  of  the  pendulum  may  be  changed 
by  turning  the  spool  so  as  to  wind  or  unwind  the  thread. 
Small  adjustments  are  easily  made  by  gently  turning  the 
spool.  To  fasten  the  thread  to  the  bullet,  cut  a  little  lip  in 
the  bullet  with  a  knife,  place  the  thread  under  the  lip,  and  /"~*~\ 
smooth  the  lip  down  with  the  handle  of  the  knife.  Cut  off  v^ ) 

the  short  end  of  the  thread  close  to  the  bullet.     A  watch 

,      .  ,  .      ,  FIG.  46. 

having  a  second  hand  is  also  necessary. 

Directions.  Taking  the  lower  end  of  the  slot  of  the 
screw  as  the  center  of  suspension,  make  the  pendulum 
36cm  long.  Fill  the  slot  with  beeswax  so  that  the  thread 
will  not  move  in  the  slot.  Draw  the  bob  about  5cm  to 


THE   PENDULUM.  159 

one  side  and  release  it.  The  pendulum  should  swing 
parallel  to  the  wall  to  which  the  support  of  the  pendulum 
is  fastened.  Glance  at  the  watch  and  at  the  pendulum. 
When  the  pendulum  is  just  starting  to  return  from  the 
end  of  its  swing,  take  the  time.  Count  accurately  for 
one  minute  the  number  of  vibrations.  Record  the  num- 
ber of  vibrations.  Double  the  amplitude  of  vibration  (by 
drawing  the  bob  at  the  start  about  10cm  to  one  side)  and 
count  the  number  of  vibrations  for  another  minute. 

What  effect  has  a  change  of  amplitude  on  the  number 
of  vibrations  performed  by  a  pendulum  in  a  minute  ? 

Experiment  7O.  To  find  the  effect  a  change  of  length  in 
a  pendulum  has  upon  the  number  of  vibrations  performed 
in  a- minute. 

Apparatus.     The  same  as  in  the  last  experiment ;  a  long  pole. 

Directions.  Place  one  end  of  the  long  pole  on  the 
floor,  so  that  the  pole  shall  stand  in  a  vertical  position 
with  its  side  against  the  screw.  Mark  on  the  pole  the 
position  of  the  center  of  suspension ;  then,  starting  from 
this  point,  measure  off  on  the  pole  a  distance  of  225cm. 
Put  the  pole  in  the  vertical  position  as  before  and  adjust 
the  bob  till  the  pendulum  is  225cm  long. 

Using  one  amplitude,  record,  as  before,  the  number  of 
vibrations  for  one  minute.  Then  make  the  length  of  the 
pendulum  100cm,  and  record  the  number  of  vibrations  for 
one  minute.  Finally  make  the  pendulum  25cm  long,  and 
record  as  before. 

Divide  the  greatest  length  of  the  pendulum  by  the  least. 
Divide  the  largest  number  of  vibrations  by  the  smallest. 

Is  there  any  agreement  between  the  quotients  ? 


160  EXPERIMENTAL   PHYSICS. 

Does  taking  the  square  root  of  one  of  the  quotients 
make  the  values  approximately  equal  ? 

What  is  the  relation  between  the  lengths  of  pendulums 
and  the  number  of  vibrations  ? 

QUESTIONS.  From  an  inspection  of  your  results,  answer  the  following 
questions :  What  is  the  length  of  a  pendulum  that  will  beat  seconds  ? 
half  seconds  ? 

Experiment  71.  To  find  whether  the  weight  and  material 
of  the  pendulum  bob  have  any  effect  on  the  number  of  vibra- 
tions in  a  minute. 

Apparatus.     The  same  as  in  Exp.  69 ;  a   marble  of  about  the 

same  size  as  the  bullet. 

* 

Directions.  Jn  place  of  the  bullet,  fasten  the  marble 
to  the  end  of  the  silk  thread  by  means  of  beeswax.  Make 
the  pendulum  36cm  long.  Record  the  number  of  vibra- 
tions per  minute. 

Compare  the  result  with  that  recorded  in  Exp.  69. 

What  is  your  conclusion  ? 


EXAMPLES. 

1.  If  a  pendulum  makes  30  vibrations  in  a  minute,  how  many  oscilla- 
tions does  it  make  in  2  minutes  ?     How  many  oscillations  does  the  pen- 
dulum make  in  a  second  ? 

2.  If  a  pendulum  makes  40  vibrations  in  a  minute,  what  is  the  time 
of  a  single  vibration  ? 

3.  If  a  pendulum  25cm  long  makes  60  vibrations  in  a  minute,  what 
must  be  the  length  of  a  pendulum  in  order  that  it  shall  make  10  vibra- 
tions in  a  minute  ? 

Solution.  As  the  number  of  vibrations  of  two  pendulums  are  to  each 
other  inversely  as  the  square  roots  of  the  lengths  of  the  pendulums,  we 
have,  if  we  denote  by  x  the  required  length. 


VELOCITY   OF   SOUND.  161 


60  :  10  =  \lx  : 
10  Vx  =  60  V25 
Vz  =  6  V25 
.-.  x  =  900 
Hence  the  required  length  is  900cm. 

4.  If  a  pendulum  lm  long  vibrates  once  in  a  second,  what  must  be  the 
length  of  a  pendulum  in  order  that  it  shall  oscillate  once  in  a  minute  ? 

5.  If  a  pendulum  4  units  in  length  makes  a  vibration  in  0.3  second, 
find  the  length  of  a  pendulum  that  makes  a  vibration  in  1.8  seconds. 

6.  If  a  pendulum  6  units  in  length  makes  an  oscillation  in  5  seconds, 
what  will  be  the  time  of  an  oscillation  of  a  pendulum  0.54  units  in  length  ? 


VELOCITY    OP    SOUND. 

65.  The  Velocity  of  Sound  in  Air.  Our  next  experi- 
ment will  be  for  the  purpose  of  getting,  roughly,  the 
velocity  of  sound  in  air  ;  of  getting,  in  other  words,  the 
distance  that  sound  will  travel  in  one  second. 

Experiment  72.     To  find  the  velocity  of  sound  in  air. 

Apparatus.  A  wooden  support  like  the  one  used  in  Exp.  28  ;  a 
bullet  ;  a  piece  of  silk  thread  ;  a  stool  ;  two  small  boards  ;  a  small 

spy-glass. 

Directions.  This  experiment  is  to  be  performed  out 
doors  in  an  open  space,  where  a  distance  of  500  feet 
should  be  measured  off.  At  the  spot  from  which  the  dis- 
tance is  measured  the  observer  with  the  spy-glass  should 
stand;  at  the  spot  500  feet  away  the  support  should  be 
placed. 

By  means  of  clamps  fasten  to  the  support  a  pendulum 
of  such  length  that  it  will  beat  half  seconds.  (See  your 
record  of  Exp.  70.)  That  the  bob  may  be  seen  as  it 
swings  back  and  forth,  pin  a  piece  of  white  paper  about 


162  EXPERIMENTAL   PHYSICS. 

20cm  SqUare  on  the  upright  behind  the  pendulum.  The 
student  beside  the  support  starts  the  pendulum  swinging, 
taking  care  to  have  it  swing  only  a  little  way  from  side 
to  side;  if  it  swings  off  the  paper,  the  observer  looking 
through  the  spy-glass  cannot  see  the  pendulum.  When 
the  pendulum  reaches  one  extremity  of  its  swing,  the 
student  standing  beside  the  support  strikes  the  boards 
together.  If  the  sound  reaches  the  ear  of  the  student 
looking  through  the  spy-glass,  at  the  instant  in  which  the 
pendulum  reaches  the  other  extremity  of  its  swing,  then 
it  has  taken  the  sound  just  0.5  second  to  travel  500 
feet.  In  order  that  the  student  at  the  spy-glass  may 
have  a  good  many  opportunities  to  observe  the  pendu- 
lum and  listen  to  the  sound,  the  student  beside  the  sup- 
port should  strike  the  boards  together  every  time  the 
pendulum  gets  to  the  end  of  its  swing  next  to  him.  By 
moving  the  spy-glass  from  or  towards  the  pendulum,  the 
distance  that  the  sound  will  travel  in  0.5  second  can  be 
found. 

Interchange  the  spy-glass  and  the  pendulum;  then 
repeat  the  experiment,  the  student  who  before  looked 
through  the  spy-glass  now  taking  his  position  beside  the 
support.  For  the  velocity  of  sound  in  air,  take  the  aver- 
age of  the  two  distances  found. 

From  your  observations  on  the  velocity  of  sound  per  0.5 
second,  what  is  the  velocity  of  sound  per  second  in  feet  ? 

QUESTION.  If  there  are  15,240cm  in  500  feet,  what  is  the  velocity  of 
sound  per  second  in  centimeters  ? 

Experiment  73.  To  find  whether  the  air  is  necessary 
for  the  transmission  of  sound. 


VELOCITY   OF   SOUND.  163 

Apparatus.  A  Kjeldahl  flask ;  a  one-hole  rubber  stopple  to  fit 
the  flask ;  a  piece  of  pressure  tube  about  30cm  long ;  a  glass  tube 
long  enough  to  reach  to  the  middle  of  the  body  of  the  flask ;  a  little 
toy  bell ;  an  air-pump. 

Directions.  Push  the  glass  tube  through  the  stopple, 
and  over  the  end  that  goes  into  the  flask  slip  a  bit  of 
rubber  tube  about  0.5cm  long.  With  a  bit  of  thread 
fasten  the  bell  to  the  glass  tube;  the  bit  of  rubber  will 
keep  the  thread  from  slipping  off.  Over  the  other  end  of 
the  glass  tube  slip  the  pressure  tube.  Put  the  stopple  in 
place.  Shake  the  flask,  and  listen  to  hear  the  bell  ring. 
Connect  the  flask  to  the  air-pump  by  means  of  the  rubber 
tube.  Pump  out  a  little  air,  and  shake  the  flask. 

Is  the  sound  of  the  bell  fainter  than  before  ? 

Pump  out  some  more  air. 

On  shaking  the  flask,  can  you  hear  the  bell  ? 

What  inference  can  you  draw  from  this  experiment? 

Point  out  in  what  way  you  have  used  the  method  of 
'differences  in  this  experiment. 

Can  sound  pass  through  a  vacuum  ? 

Experiment  74.  To  find  whether  a  musical  sound  can 
be  produced  by  a  vibrating  body  beating  the  air  at  regular 
intervals. 

Apparatus.    A  straight  piece  of  clock-spring  about  50cm  long ;  a  vise. 

Directions.  Fasten  the  clock-spring  in  the  vise  with 
about  45cm  projecting  horizontally.  Set  the  spring  vibrat- 
ing horizontally  through  a  small  arc,  and  record  the  num- 
ber of  vibrations  made  in  0.5  minute.  Then  set  the  spring 
swinging  through  a  large  arc,  and  record  the  number  of 
vibrations  made  in  0.5  minute. 


164  EXPERIMENTAL    PHYSICS. 

Does  the  time  of  vibration  of  the  spring  depend  upon 
the  amplitude  of  vibration  ? 

Push  the  spring  farther  into  the  vise  leaving  about  20cm 
projecting.  If  possible,  make  observations  and  record  as 
before. 

What  is  your  inference  ? 

Leave  only  about  8cm  projecting,  and  finally  only  about 

_J.cm 

When  the  spring  now  vibrates,  does  it  give  a  musical 
sound  ? 

Does  the  pitch  become  higher  or  lower  as  the  number 
of  vibrations  increases  ? 

From  the  results  of  this  experiment,  should  you  say 
that  a  musical  sound  has  been  produced  by  a  vibrating 
body  beating  the  air  at  regular  intervals  ? 

TUNING-FORK. 

66.  The  Tuning-Fork.  The  tuning-fork  is  an  acous- 
tic instrument  of  great  interest.  The  spring  of  the 
preceding  experiment  serves  as  a  starting-point  in  the 
description  of  the  tuning-fork,  which  may  be  looked  upon 
as  an  elastic  bar  bent  into  a  U-shape,  free  at  both  ends, 
and  supported  in  the  middle  where  the  stem  or  handle  is 
inserted.  Tuning-forks  are  usually  made  of  steel.  The 
tuning-fork  is  excited  (set  in  vibration)  by  striking  the 
outside  of  one  of  the  prongs  against  a  board  covered  with 
leather  or  flannel,  but  never  against  a  table  or  other  hard 
object.  Shortly  after  the  fork  has  been  excited,  its  tone 
becomes  pure  and  simple. 

NOTE.  The  tuning-fork  was  invented  in  1711,  by  John  Shore,  a  trump- 
eter in  the  service  of  George  I.  of  England. 


TRANSMISSION    OF    SOUND.  165 


TRANSMISSION    OF    SOUND. 

67.    Mode  of  Transmission  of  Sound  in  Air.     It  was 

learned  in  Exp.  73  that  the  presence  of  air  was  necessary 
for  the  transmission  of  sound  from  a  bell  to  the  ear.  But 
an  inquiry  of  importance  is,  how  the  sound  is  transmitted 
by  the  air,  by  a  puff,  that  is,  by  a  small  gust  of  air  in 
which  the  air  particles  are  sent  from  the  sounding  body 
to  the  ear,  or  by  a  pulse,  that  is,  to-and-fro  motion,  of  the 
air  particles.  The  object  of  the  next  experiment  is  to 
satisfy  this  inquiry. 

Experiment  75.  To  find  whether  the  movement  of  air, 
when  sound  passes  through  it,  is  of  the  nature  of  a  puff  or  of 
a  pulse. 

Apparatus.  A  long  tin  tube  that  tapers  at  one  end ;  a  candle ; 
touch-paper.1 

Directions.  Place  the  tube  in  a  horizontal  position  on 
the  table.  At  the  small  end  put  the  lighted  candle  (see 
Fig.  47),  carefully  shielded  from  air  currents,  with  the 
flame  opposite  the  opening  and  but  2cm  or  3cra  away. 
Get  a  student  to  strike  together  two  blocks  of  wood  at 
the  large  opening. 

What  happens  to  the  flame  ? 

Is  the  flame  affected  thus  by  a  puff  or  by  a  pulse  of  air  ? 

To  answer  this  question,  having  filled  the  tube  with 
smoke  by  burning  touch-paper  in  it,  strike  the  blocks 
together  and  watch  the  appearance  at  the  small  end  of 

1  Touch-paper  is  made  by  soaking  filter  paper  or  blotting  paper  in  a 
saturated  solution  of  nitrate  of  potash,  and  then  drying  the  paper. 


166  EXPERIMENTAL  PHYSICS. 

the  tube.  The  purpose  of  the  smoke  is  to  make  visible 
to  the  eye  the  currents  of  air,  if  any,  that  are  set  in 
motion  by  clapping  the  blocks  together.  To  see  what 


FIG.  47. 

appearance  a  puff  of  air  would  produce,  let  the  student  at 
the  larger  end  of  the  tube  blow  into  the  tube  with  a  quick 
short  puff. 

From  the  behavior  of  the  smoke  when  the  blocks  are 
struck  together,  should  you  say  that  the  candle  had  been 
affected  by  a  puff  of  air  or  by  a  pulse  ? 

68.  Is  Sound  a  Wave-Motion  of  Air  ?  From  Exp.  73 
you  have  already  learned  that  the  presence  of  air  is  neces- 
sary for  the  transmission  of  sound,  and  from  Exp.  75  you 
have  seen  that  when  conveying  sound,  the  particles  of  air 
have  a  back-and-forth  motion.  Can  this  motion  be  a 
wave-motion  of  air?  To  prepare  yourself  for  answering 
this  question,  recall  your  study  of  water  waves  and  the 
idea  you  gained  of  what  is  meant  by  interference  (see 
pages  156  and  157).  By  the  interference  of  two  sets  of 
water  waves,  there  were  produced  waves  of  different  sizes, 
from  very  small  ones  up  to  waves  of  greater  magnitudes 


TRANSMISSION   OF    SOUND.  167 

than  those  of  either  of  the  original  set  of  waves;  calms 
were  also  produced.  If  sound  is  really  due  to  a  wave- 
motion  of  the  air,  phenomena  of  interference  ought  to  be 
observed  under  suitable  conditions.  In  the  interference 
of  sound  waves,  silence  would  correspond  to  a  calm  in 
the  interference  of  water  waves,  and  varying  degrees  of 
loudness  of  sound  to  water  waves  of  different  heights. 
The  object  of  the  next  experiment  is  the  study  of  sound 
under  different  phases,  with  a  view  to  determining  whether 
phenomena  of  interference  can  occur. 

Experiment  76.  To  find  whether  the  phenomena  of  inter- 
ference can  be  observed  in  sound. 

Apparatus.  A  tuning-fork  ;  a  100CC  graduate  ;  a  cylinder  of  card- 
board about  as  long  as  one  of  the  prongs  of  the  tuning-fork  and 
about  2cm  in  diameter ;  a  tuning-fork,  high  C. 

Directions.  By  striking  one  prong  of  the  tuning-fork 
against  a  piece  of  leather  laid  upon  the  table,  set  the  fork 
in  vibration.  Then  hold  the  fork  above  the  graduate  in 
such  a  position  that  the  ends  of  the  prongs  lie  in  the  axis 
of  the  graduate.  Pour  water  slowly  into  the  graduate. 
As  the  water  rises,  the  sound  grows  louder;  and  then  as 
more  water  is  added,  the  sound  grows  weaker.  In  this 
experiment  adjust  the  level  of  the  water  till  the  sound  of 
the  fork  is  strongly  reinforced.  Turn  the  fork  slowly 
round  its  axis. 

For  certain  positions  of  the  fork,  do  the  sounds  become 
nearly  inaudible  ? 

If  any  such  positions  are  found,  hold  the  fork  steadily 
in  one  of  them,  and  then  carefully  slide  the  cardboard 
cylinder  over  one  of  the  prongs,  as  shown  in  Fig.  48, 


168  EXPERIMENTAL   PHYSICS. 

without  allowing  the  cylinder  to  touch  either  prong,  as 
that  would  interrupt  the  vibrations. 

Is  the  sound  restored? 

Could  you  account  for  what  you  observe  by  regarding 
each  prong  of  the  fork  as  sending  out  sound,  but  as  one 
of  the  prongs  is  nearer  the  mouth 
of  the  graduate  than  the  other, 
the  sound  reflected  by  the  surface  of  the  water 
in  the  graduate  interferes  with  the  sound  from 
the  more  remote  prong? 

On  the  whole,  what  is  your  conclusion  from 
this  experiment? 

69.  Form  of  a  Sound  Wave.  If  a  bell  is 
sounded,  the  tone  of  the  bell  is  heard  above, 
below,  at  one  side,  and,  in  fact,  at  any  point 
the  ear  may  be  placed.  The  sound  spreads  out, 
then,  in  spheres  whose  common  center  is  the 

FIG.  48. 

position  of  the  bell.  The  sound  wave  is  made 
up  of  a  condensed  portion  (where  the  particles  are  crowded 
together),  corresponding  to  the  crest  of  a  water  wave,  and 
of  a  rarefied  portion  (where  the  particles  of  air  are  farther 
apart  than  usual),  corresponding  to  the  trough  of  a  water 
wave.  Where  a  condensed  portion  of  a  sound  wave  coin- 
cides with  the  rarefied  portion  of  another  equal  wave, 
silence  results;  where  the  condensed  portion  coincides 
with  condensed  portion,  and  rarefied  portion  coincides 
with  rarefied  portion,  a  sound  louder  than  that  due  to 
either  wave  is  produced. 

Between  what  points  do  you  measure  the  length  of  a 
sound  wave  ? 


RAPID    VIBRATIONS.  169 

The  diagram  (Fig.  49)  represents  the  concentric  waves 
of  sound  spreading  from  the  point  of  disturbance  at  the 
center.  Where  the  __  _  _ 

circles  of  dots  are 
nearest  together, 
there  is  the  con- 
densed portion  of 
the  wave ;  where  the 
circles  of  dots  are 
farthest  apart,  there 


the   rarefied  por-     ^  \  V^Cr. 

>n  of  the  wave.  \^\\\\  X<^xr~ 

In  the  propagation  ^x^\  <>  ^ *• 

of  water  waves  the  v^^^or-  ^i  ~  :-- 

NS^S^-.-^rrr^j 
motion  of  the  water  ^^T?:3=S^ 

particles   is    to  and 

FIG.  49. 

fro  at  right  angles 

to  the  direction  in  which  the  wave  moves. 

In  the  case  of  sound  waves  in  air,  do  the  air  particles 
move  to  and  fro  at  right  angles  to  the  direction  in  which 
the  sound  travels  ? 


RAPID    VIBRATIONS. 

7O.    Method  of  Counting-  Rapid  Vibrations.     In  the 

experiment  with  the  clock-spring  clamped  in  the  vise, 
you  saw  that  by  shortening  the  spring  the  musical  sound 
emitted  increased  in  sharpness,  or  pitch,  and  you  also  ob- 
served that  the  vibrations  became  so  rapid  that  the  eye 
could  not  follow  them  quickly  enough  to  count  them.  In 
the  next  experiment  we  shall  find  how  many  vibrations  per 


170 


EXPERIMENTAL   PHYSICS. 


second  a  certain  tuning-fork  makes.  In  this  experiment 
a  piece  of  smoked  glass  is  drawn  beneath  a  vibrating  pen- 
dulum (Fig.  50)  and  a  vibrating  tuning-fork.  A  little 


FIG.  so. 


style,  made  of  a  bristle,  is  fastened  to  the  pendulum  and 
another  to  the  fork.  These  styles  trace  out  curves  on  the 
glass  as  shown  in  Fig.  51.  The  wavy  line  is  traced  by 


FIG.  51. 

the  style  attached  to  the  tuning-fork,  while  the  other  lines 
are  traced  by  the  style  attached  to  the  pendulum. 

Experiment  77.     To  find  the  number  of  vibrations  made 
in  a  second  by  a  tuning-fork. 


RAPID   VIBRATIONS.  171 

Apparatus.  A  tuning-fork,  middle  C  ;  a  piece  of  apparatus  pro- 
vided with  a  support  for  the  tuning-fork  and  the  pendulum ;  a  watch ; 
a  bass-viol  bow  ;  rosin  ;  a  rectangular  piece  of  glass. 

Directions.  Clean  the  glass,  and  then  slightly  smoke 
it  by  holding  it  in  an  ordinary  flame.  Lay  the  glass  on 
the  carrier  beneath  the  pendulum.  To  the  little  rod  pro- 
jecting from  the  lower  side  of  the  pendulum  bob  fasten, 
by  means  of  thread,  a  flexible  bristle  whose  end  shall 
bear  lightly  on  the  surface  of  the  glass,  so  that,  as  the 
pendulum  swings,  a  line  shall  be  traced  in  the  thin  layer 
of  soot  which  covers  the  glass.  Near  the  end  of  one 
prong  of  the  tuning-fork  a  somewhat  stiffer  bristle  should 
be  fastened  by  a  bit  of  wax.  This  bristle  should  lightly 
touch  the  glass,  to  whose  surface  it  should, be  somewhat 
inclined.  Find  how  many  vibrations  the  pendulum  makes 
in  a  minute. 

How  long  does  it  take  the  pendulum  to  make  one 
vibration  ? 

Now  place  the  tuning-fork,  mounted  on  its  support,  in 
a  position  to  bring  the  end  of  the  bristle  attached  to  it  as 
close  as  practicable  beside  that  attached  to  the  pendulum. 
When  both  pendulum  and  fork  are  vibrating,  the  bristles 
should  move  parallel  to  each  other.  When  all  the  adjust- 
ments are  made,  set  the  pendulum  swinging,  excite  the 
fork  by  drawing  the  bow,  which  has  been  well  rosined, 
across  it;  then  draw  the  carrier  holding  the  glass  plate 
along  at  right  angles  to  the  direction  in  which  the  pendu- 
lum and  fork  are  vibrating. 

Remove  the  glass,  count  carefully,  using  a  magnify- 
ing glass  if  necessary,  the  number  of  vibrations  recorded 
by  the  fork  on  the  glass  between  the  points  corre- 


172  EXPERIMENTAL    PHYSICS. 

spending  to  one  vibration  of  the  pendulum.  Record 
this  number. 

We  already  know  the  time  the  pendulum  takes  to  make 
one  vibration,  and  we  have  just  found  the  number  of  vibra- 
tions the  fork  makes  in  an  equal  length  of  time'. 

How  many  vibrations  does  the  middle  C  tuning-fork 
make  in  a  second  ? 

TUNING-FORK    AND    RESONATOR. 

71.  The  Determination  of  the  Velocity  of  Sound  in 
Air  by  means  of  the  Tuning-Fork  and  Resonator.  If 

we  know  the  number  of  vibrations  which  a  tuning-fork 
makes  in  a  second  and  the  length  of  a  column  of  air  that 
will  reinforce  the  tone  of  the  fork  as  in  Exp.  76,  we  can 
compute  from  these  data  the  velocity  of  sound  in  air. 
The  object  of  the  next  experiment  is  to  obtain  the  data 
and  make  the  computation. 

Experiment  78.  To  find,  by  means  of  a  resonance  tube, 
the  velocity  of  sound  in  air. 

Apparatus.  A  glass  jar  35cm  or  more  in  depth,  and  from  3cm  to 
10cm  in  diameter  ;  a  tuning-fork,  middle  C  ;  a  thermometer. 

Directions.  Place  the  jar  on  the  table,  and  over  its 
mouth  hold  the  vibrating  tuning-fork  with  the  ends  of  its 
prongs  in  line  with  the  axis  of  the  jar.  Pour  water  grad- 
ually into  the  jar  until  the  sound  of  the  fork  is  strongly 
reinforced.  By  pouring  in  a  little  more  water,  or  by 
pouring  out  a  little,  get  the  length  of  the  air  column  from 
the  mouth  of  the  jar  to  the  surface  of  the  water  such  that 
the  sound  will  be  the  very  loudest.  Then  measure  and 


TUNING-FORK   AND    RESONATOR.  173 

record  in  centimeters  the  distance  from  the  mouth  of  the 
jar  (Fig.  52)  to  the  level  of  the  water;  also  record  the 
diameter  of  the  jar  in  centimeters. 

Instead  of  pouring  water  into  the  jar,  the  level  of  the 
water  may  be  readily  changed  by  means  of  a  siphon,  con- 
sisting of  two  glass  tubes  of  small  bore  joined  by  a  rubber 
tube.  One  of  the  glass  tubes  is 
bent  so  that  it  will  reach  nearly 
to  the  bottom  of  the  jar  when  hung  over  its 
edge,  the  other  glass  tube  is  bent  to  hang  over 
the  edge  of  a  jar  containing  a  supply  of  water. 
The  rubber  tube  is  long  enough  to  allow  the 
jar  containing  the  supply  of  water  to  be  raised 
or  lowered  so  that  water  will  flow  into  the 
other  jar  or  out  of  it,  thus  raising  or  lowering 
the  level. 

Record  the  temperature  of  the  air  in  the  jar. 

The  forward  motion  of  the  fork  sent  down 
the  tube  an  impulse  which,  at  the  surface  of  FlG  52 
the  water,  was  reflected  in  time  to  reinforce 
the  impulse  given  by  the  fork  in  its  backward  motion. 
Thus  during  the  forward  motion  of  the  fork,  that  is, 
during  half  a  vibration,  the  sound  traveled  to  the  water 
and  back.  When  the  sound  passes  through  the  mouth 
of  the  jar,  a  spreading  of  the  sound  occurs,  so  it  is  found 
necessary  to  add  to  the  distance  which  the  sound  travels 
in  one-fourth  of  a  vibration  (that  is,  to  the  distance  from 
the  mouth  of  the  jar  to  the  level  of  the  water)  one-fourth 
of  the  diameter  of  the  jar. 

After  making  this  correction,  what  distance  do  you  find 
that  sound  travels  during  one  vibration  of  the  fork  ? 


174  EXPERIMENTAL   PHYSICS. 

From  the  experiment  you  have  already  performed, 
how  many  vibrations  does  the  tuning-fork  make  in  a 
second  ? 

From  your  data,  what  is  the  velocity  in  centimeters  per 
second  of  sound  in  air? 

72.  Sympathetic  Vibrations.  In  the  last  experiment 
the  fork  was  able  by  its  vibrations  to  set  into  vibration  a 
column  of  air  of  definite  length,  and  thereby  the  loudness 
of  its  note  was  greatly  increased.  The  air  column,  when  of 
proper  length,  vibrated  in  sympathy  with  the  fork;  hence 
such  vibrations  are  called  sympathetic  vibrations. 

In  most  sonorous  bodies  (for  example,  a  tuning-fork) 
mechanical  movement  (the  motion  of  the  prongs  of  a 
tuning-fork,  for  instance)  is  transformed  into  sound.  It 
would  be  interesting  to  inquire  whether  this  process  has 
ever  been  reversed ;  whether,  in  other  words,  sound  vibra- 
tions can  generate  mechanical  motion.  There  is  a  little 
instrument,  known  as  a  sound  radiometer,  or  an  acoustic 
reaction  wheel,  which  can  be  kept  in  motion  by  sound.  It 
is  made  of  four  small  tubes  open  at  one  end.  These  tubes, 
made  of  aluminum  on  account  of  its  lightness,  are  accu- 
rately tuned  to  the  same  note.  Two  light  rods  or  wires 
are  fastened  together  at  right  angles,  making  four  arms  of 
equal  length.  A  tube,  or  resonator,  is  fastened  at  the 
middle  of  its  length  to  the  extremity  of  each  arm  in  such 
a  way  that  its  axis  lies  in  a  plane  below  but  parallel  to 
that  of  the  crossed  wires.  The  whole  is  delicately  poised 
on  a  pivot  in  a  horizontal  position.  When  this  instrument 
is  put  near  a  fork  giving  the  same  note  as  that  to  which 
the  resonators  are  tuned,  the  little  wheel  begins  to  rotate, 


TUNING-FORK   AND    RESONATOR.  175 

and  continues  in  rotation  as  long  as  the  tuning-fork  con- 
tinues in  vibration. 


73.  Beats.  If  two  tuning-forks,  one  of  which  makes 
254  vibrations  while  the  other  makes  255,  are  set  in 
motion,  a  peculiar  palpitating  effect  results,  produced  by 
bursts  of  sound,  separated  from  one  another  by  intervals 
of  comparative  silence.  These  bursts  of  sound  are  called 
beats.  By  the  principle  of  interference  (see  Exp.  76)  the 
production  of  beats  can  be  fully  explained.  Suppose  the 
forks  to  be  in  vibration ;  if  we  start  from  the  time  when 
the  condensed  portion  of  the  waves  from  each  fork  reaches 
the  ear  at  the  same  instant,  that  is,  when  the  sound  is 
loudest,  just  one  second  will  elapse  before  the  sound 
is  loudest  again.  The  fork  making  255  vibrations  per 
second  gains  a  vibration  in  one  second  over  the  other  fork, 
that  is,  in  one  second  the  note  from  this  fork  gains  one 
wave-length ;  but  since  at  the  middle  of  the  second  it  has 
gained  only  half  a  wave-length,  the  rarefied  portion  of  the 
sound  wave  from  this  fork  combines  with  the  condensed 
portion  of  the  sound  wave  from  the  other  fork,  the  two 
portions  neutralize  each  other,  and  silence  results.  Dur- 
ing every  second,  then,  that  passes  while  the  forks  are 
vibrating  together,  there  will  be  one  beat  and  one  period  of 
silence.  If  one  fork  had  made  254  vibrations  per  second 
and  the  other  256,  two  beats  and  two  periods  of  silence 
would  have  occurred  during  the  second. 

If,  when  two  tuning-forks  are  sounding  together,  there 
are  beats,  the  number  of  beats  per  second  tells  the  differ- 
ence between  the  number  of  vibrations  per  second  of  the 
two  forks ;  further,  if  the  number  of  vibrations  per  second 


176  EXPERIMENTAL    PHYSICS. 

of  one  of  the  forks  is  known  and  it  is  also  known  which 
of  the  forks  gives  the  higher  note,  it  is  possible  to  find 
the  number  of  vibrations  per  second  made  by  the  fork 
whose  number  of  vibrations  is  unknown.  For  example, 
two  forks  A  and  B  are  sounded  together,  and  four  beats 
per  second  are  counted.  If  it  is  known  that  A  makes  256 
vibrations  per  second,  and  that  its  note  is  lower  than  that 
of  J&,  it  follows  that  B  makes  in  one  second  260  vibrations. 

74.  Octave;    Concord;    Discord.     Two  notes  are  an 
octave  apart  when   one  is  produced  by  twice  as  many 
vibrations  as  the  other.     Thus  a  tuning-fork  that  makes 
508  vibrations  per  second  emits  a  note  which  is  the  octave 
of  the  note  given  by  a  fork  vibrating  254  times  per  second. 
When  two  notes  an  octave  apart  are  sounded  together, 
the  result  is  pleasing  to  the  ear,  and  there  is  said  to  be 
concord.     Besides  notes  an  octave  apart,  there  are  others 
that  produce  concord  when  sounded  together;  but  there 
are  many  notes  which,  on  being  sounded  at  the  same  time, 
produce  a  disagreeable  impression  on  the  ear;  such  notes 
are  said  to  produce  discord.     The  unpleasant,  jarring  effect 
of  discord  is  due  to  the  production  of  beats. 

VIBRATING    STRINGS. 

75.  Pitch  of  Vibrating  Strings.    It  will  be  the  purpose 
of  the  three  following  experiments  to  find  what  relations 
exist  between  the  length,  the  tension,  the  thickness  of  a 
stretched  wire,  and  the  number  of  vibrations  per  second. 

Experiment  79.      To  find  the  relation  between  the  length 
of  a  stretched  wire  and  the  number  of  vibrations  per  second. 


VIBRATING   STRINGS. 


177 


Apparatus.  A  spring  balance  of  30  pounds'  capacity ;  a  piece  of 
spring  brass  wire,  No.  22  B.  &  S.,  1.5m  long ;  two  of  the  triangular 
pieces  of  wood  used  in  Exp.  62  ;  a  meter  stick  ;  a  middle  C  fork,  and 
another  an  octave  higher. 

Directions.  Fasten  one  end  of  the  wire  to  a  screw  in 
the  table-top,  and  lay  the  wire  straight  on  the  table; 
fasten  the  other  end  to  the  balance.  Hook  the  ring  of 
the  balance  to  the  screw  for  applying  tension,  as  shown 
in  Fig.  53.  (For  Exps.  79  and  80  consider  only  the  bal- 


FlG.  53. 


ance  and  wire  which,  in  the  figure,  is  next  to  the  edge  of 
the  table.)  Under  the  wire  near  the  screw  fasten  by  a 
brad  one  of  the  prisms  with  its  edge  at  right  angles  to  the 
wire.  Under  the  wire  lay  the  other  prism  parallel  to 
the  first.  If  the  balance,  as  it  should,  holds  the  wire 
about  as  high  as  the  top  of  the  movable  prism,  this  prism 
can  be  moved  along  under  the  wire  without  changing  the 
tension  to  any  extent. 

Allowing  for  the  zero  error  of  the  balance,  when  used 
in  the  horizontal  position,  stretch  the/  wire  with  a  force 
of  20  pounds,  and,  keeping  this  tension  constant,  find  the 


178  EXPERIMENTAL   PHYSICS. 

lengths  that  will  give  notes  corresponding  to  the  two 
forks  respectively.  Set  the  wire  into  vibration  by  pluck- 
ing it  in  the  middle,  and,  with  the  ear  close  to  the  wire, 
listen  for  the  fundamental  note,  which  may  for  an  instant 
be  obscured  by  harsh  or  grating  overtones. 

A  student  who  has  no  keen  perception  of  musical  pitch 
can  secure  nearly  perfect  unison  by  sounding  the  wire  and 
the  fork  at  the  same  time ;  the  beats,  which  become  very 
apparent  when  the  sounds  are  near  unison,  will  guide  him 
in  his  judgment.  It  will  be  well  to  press  the  wire  with 
the  finger  lightly  against  the  movable  prism  so  as  to  limit 
the  vibrations  to  that  part  under  consideration. 

One  fork  is  an  octave  higher  than  the  other. 

Divide  the  greater  number  of  vibrations  by  the  smaller ; 
also  the  greater  length  of  wire  between  the  prisms  by  the 
smaller. 

Are  the  quotients  equal? 

The  inference  you  can  draw  we  shall  call  Law  1. 

State  Law  1. 

QUESTIONS.  If  a  string  100cm  long  gives  a  certain  note  when  plucked, 
what  must  be  its  length  to  give  the  note  an  octave  higher  ?  What  must 
be  its  length  to  give  the  note  an  octave  lower  ? 

Experiment  8O.  To  find  the  relation  between  the  tension 
of  a  wire  and  the  number  of  vibrations  per  second. 

Apparatus.     The  same  as  in  Exp.  79,  without  the  higher  fork. 

Directions.  Correcting  for  the  zero  error  of  the  bal- 
ance, when  in  the  horizontal  position,  make  the  tension 
5  pounds.  Find  what  length  of  wire  will  give  a  note 
whose  pitch  corresponds  to  that  of  the  middle  C  fork. 


VIBRATING    STRINGS.  179 

Turn  back  to  your  record  of  Exp.  79 ;  you  ought  to 
find  there  a  length  recorded  equal  or  nearly  equal  to  the 
one  just  found. 

To  which  fork  does  the  note  of  the  recorded  length  of 
wire  correspond? 

Divide  the  number  of  vibrations  of  this  fork  by  the 
number  of  vibrations  of  the  fork  used  in  the  present 
experiment ;  also  divide  the  tension  used  in  the  last 
experiment  by  the  tension  used  in  this  experiment. 

If  the  two  quotients  are  not  equal,  try  to  make  the 
second  equal  to  the  first  by  squaring  or  by  taking  the 
square  root. 

The  relation  thus  found  between  the  number  of  vibra- 
tions per  second  and  the  tension  is  called  Law  2. 

State  Law  2. 

QUESTIONS.  If  a  wire  under  a  tension  of  7  pounds  gives  a  certain 
note,  how  much  higher  would  the  note  become  on  increasing  the  tension 
to  28  pounds  ?  How  much  lower  would  the  note  become  if  the  tension 
were  reduced  to  1.75  pounds  ? 

Experiment  81.  To  find  the  relation  between  the  thick- 
ness of  a  wire  and  the  number  of  vibrations  per  second. 

Apparatus.  A  piece  of  spring  brass  wire,  No.  28  B.  &  S.,  stretched 
as  shown  in  Fig.  53  ;  the  fork  of  higher  pitch. 

Directions.  Correcting  as  before  for  the  zero  error  of 
the  balance,  when  used  in  the  horizontal  position,  apply  to 
the  wire  a  tension  of  5  pounds.  Find  what  length  of  wire 
will  give  a  note  whose  pitch  corresponds  to  that  of  the 
fork  of  higher  pitch. 

Turn  back  to  Exp.  80 ;  you  ought  to  find  a  length 
recorded  equal  or  nearly  equal  to  that  obtained  in  this 
experiment. 


180  EXPERIMENTAL    PHYSICS. 

Divide  the  number  of  vibrations  of  the  wire  of  this 
experiment  by  the  number  of  vibrations  of  the  wire  of 
Exp.  80.  The  ratio  of  the  thicknesses  of  the  two  wires 
is  as  2  to  1. 

If  the  ratio  of  the  thicknesses  is  not  equal  to  the  ratio 
of  the  number  of  vibrations,  try  to  make  it  equal  by  squar- 
ing or  taking  the  square  root,  inverting  if  necessary. 

The  relation  thus  obtained  between  the  thickness  of  the 
wire  and  the  pitch  is  called  Law  3. 

State  Law  3. 

QUESTIONS.  '  If  a  wire  lm  long  gives  a  note  of  a  certain  pitch,  how 
much  higher  will  be  the  pitch  of  a  note  given  by  a  wire,  of  the  same 
material  as  the  first,  of  equal  length  and  stretched  by  the  same  tension, 
but  of  only  one-half  the  thickness  ?  How  much  lower  will  the  note  be  if 
the  wire  is  twice  as  thick  ? 

NOTE.  The  strings  or  wires  which  we  have  considered  are  supposed 
to  be  of  the  same  material.  Whenever  the  material  of  two  strings,  alike 
in  all  other  respects,  differs  in  density,  there  is  a  fourth  law,  "  The  number 
of  vibrations  is  inversely  proportional  to  the  square  roots  of  the  densities." 

76.  JLoudness ;  Pitch ;  Quality.  The  loudness  of  a 
note  depends  upon  the  amplitude  of  vibration.  When 
a  tuning-fork  is  set  in  vibration,  the  note,  loud  at  first, 
gradually  dies  away,  becoming  fainter  and  fainter  as  the 
amplitude  of  the  fork's  vibrations  decreases.  The  pitch 
of  a  note  depends  not  upon  the  amplitude  of  vibration, 
but  upon  the  number  of  vibrations  made  in  a  given  time : 
the  greater  the  number  of  vibrations,  the  higher  the  pitch ; 
the  smaller  the  number,  the  lower  the  pitch.  The  quality 
of  a  note  depends  neither  upon  the  amplitude  of  vibration 
nor  upon  the  frequency  of  the  vibrations,  but  upon  the 
peculiar  tones  which  accompany  the  production  of  the 
fundamental  note.  On  hearing  C  sounded  on  a  piano 


THEORY    OF    SOUND.  181 

and  then  on  a  violin,  the  ear  perceives  that  the  pitch  is 
the  same,  yet  it  distinguishes  between  the  note  emitted  by 
the  piano  and  that  given  by  the  violin ;  a  note  sounded 
on  a  piano  has  a  different  quality  from  that  of  the  same 
note  sounded  on  a  violin.  To  illustrate  the  modification 
the  fundamental  note  undergoes  by  the  peculiar  tones, 
depending  upon  the  kind  of  musical  instrument  used,  let 
the  student  imagine,  what  is  so  often  seen  at  the  sea- 
shore, long  swelling  waves  coming  from  the  sea,  whose 
surface  except  for  these  waves  is  unbroken.  These 
waves  may  be  taken  to  represent  the  fundamental  note. 
Now  suppose  a  light  breath  of  air  disturbs  slightly  the 
surface  of  these  waves,  which  become  dimpled.  The 
wavelets  thus  produced  modify  to  a  very  limited  extent 
the  character  of  the  original  waves.  So  with  musical 
instruments,  each  instrument  gives  out  the  fundamental 
note,  C  for  example,  which  is  the  same  for  them  all ;  but 
each  instrument  by  reason  of  peculiarities  of  its  construc- 
tion gives  out  little  notes,  faint  to  be  sure,  but  sufficient, 
nevertheless,  to  modify  the  fundamental  note  and  give  to 
it  an  appearance  or  quality  different  from  the  correspond- 
ing note  of  some  other  instrument. 

THEORY    OP    SOUND. 

77.  Sketch  of  the  Development  of  the  Theory  of 
Sound.  More  than  two  thousand  years  ago  Pythagoras1 

]  Pythagoras  (pronounced  py-thag'o-ras)  (about  569-500  B.C.)  founded 
a  school  of  philosophy  whose  members  in  honor  of  their  teacher  were 
called  Pythagoreans  (pronounced  py-thag-o-re'ans).  This  school  busied 
itself  with  many  fantastic  mathematical  and  philosophical  speculations, 


182  EXPERIMENTAL    PHYSICS. 

invented  the  monochord,  an  instrument  similar  to  that 
used  in  the  last  three  experiments.  With  this  instrument 
Pythagoras  made  several  discoveries  about  the  sounds 
produced  by  a  stretched  string  when  vibrating.  One  of 
his  first  discoveries  was  that  a  string  which  gives  a  cer- 
tain note  will  give  a  note  an  octave  higher,  if  the  string  is 
made  one-half  as  long. 

Very  little  advance  was  made  from  the  time  of  Pythag- 
oras till  that  of  Mersenne,1  who  proved  experimentally 
that  the  number  of  vibrations  is  inversely  proportional  to 
the  length  of  the  string ;  that  the  number  of  vibrations  of 
a  string  is  proportional  to  the  square  root  of  its  tension ; 
and  that  the  number  of  vibrations  is  inversely  proportional 
to  the  thickness  of  the  string. 

The  laws  of  vibrating  strings  have  been  determined 
mathematically  as  well  as  experimentally.  It  was  La- 
grange  2  who  completed  the  work  from  the  mathematical 
point  of  view  at  which  his  predecessors  had  labored  so 
industriously. 

It  was  reserved,  however,  for  Helmholtz,  a  very  emi- 
nent physiologist,  physicist,  and  mathematician,  to  lay 
the  foundation  of  musical  science,  which  he  accomplished 
about  the  middle  of  the  nineteenth  century. 

the  most  famous  of  which  was  the  doctrine  of  "the  harmony  of  the 
spheres."  According  to  this  doctrine,  the  heavenly  bodies  in  their 
motion  through  the  sky  give  out  grand  and  wonderful  music,  but  so  fine 
and  delicate  that  our  ears,  accustomed  to  the  gross  sounds  immediately 
around  us,  are  deaf  to  this  "  music  of  the  spheres." 

1  Mersenne  (pronounced  mer-seri)  (1588-1648)  was  a  Franciscan  friar. 
He  has  been  called  the  "  Father  of  Acoustics." 

2  Lagrange  (pronounced  la-gronzh)  (1738-1815)  was  a  celebrated  French 
mathematician, 


LAWS.  183 


LAWS. 

78.  Laws  of  Nature ;  Theory.  The  laws  of  nature 
are  general  truths  which  have  been  found  by  diligent 
search  among  the  facts  obtained  by  observation  and  exper- 
iment. For  example,  that  "  the  deflection  of  a  rod  is  pro- 
portional to  the  load  "  is  a  law,  or  general  truth,  which  all 
rods,  provided  the  load  is  not  too  great,  obey.  A  law  of 
nature,  it  must  be  remembered,  differs  from  a  law  for  the 
government  of  society;  the  former  is  fixed  and  change- 
•less,  while  the  latter  lasts  only  till  men  see  fit  to  repeal 
or  amend  it. 

From  the  results  of  your  work  in  the  laboratory,  name 
fifteen  laws  which  you  have  inferred.  If  now  you  go 
through  the  process  of  reasoning  by  which  you  arrived 
at  these  laws,  is  there  any  instance  in  which  you  did 
not  infer  a  law  from  particular  cases?  For  the  sake 
of  illustration  take  the  law  just  quoted ;  by  reference  to 
your  record  you  will  see  that  there  were  from  twelve 
to  sixteen  particular  cases  among  which  there  seems 
to  be  this  bond,  or  uniform  relation,  "the  deflection  of 
a  rod,  in  each  case,  is  proportional  to  the  load."  Life 
would  be  far  too  short  to  test  every  rod  to  see  if  this  rela- 
tion holds,  so  from  his  experience  in  a  few  particular  cases 
the  student  infers  it  to  be  true  in  all.  The  belief  in  the 
truth  of  his  inference  is  strengthened  by  the  answers 
given  by  nature  to  other  inquiring  students.  The  student 
must  not  suppose  that  the  confidence  of  men  of  science  in 
the  true  statement  of  the  laws  of  nature  rests  on  infer- 
ences from  data  so  imperfect  as  those  obtained  in  our  own 
laboratory  work.  Our  data  may  suggest  the  possibility 


184  EXPERIMENTAL    PHYSICS. 

of  the  law,  but  the  physicist  is  not  satisfied  with  this ; 
he  makes  accurate  measurements,  he  varies  the  different 
cases,  he  performs  different  experiments,  till  he  accumu- 
lates a  large  amount  of  evidence  from  which  to  draw  his 
inferences. 

When  we  speak  of  the  theory  of  sound,  we  mean  the 
general  and  accurate  knowledge  of  the  laws  of  sound, 
just  as  when  we  speak  of  the  theory  of  quadratic  equa- 
tions we  mean  the  general  and  accurate  knowledge  of  the 
laws  which  connect  the  coefficients  and  the  constant  term 
with  the  roots. 

The  term  theory,  however,  is  ambiguous;  sometimes  it 
has  the  meaning  just  given,  at  others  it  is  synonymous 
with  the  term  hypothesis. 


FALLACIES. 

79.  Fallacies  of  Observation.  In  Art.  29  the  atten- 
tion of  the  student  was  called  to  the  importance  of  dis- 
tinguishing between  facts  and  inferences.  In  this  matter 
too  much  attention  and  care  cannot  be  given  to  training 
the  mind  to  careful  habits  of  discrimination.  With  the 
best  of  intentions  of  telling  the  truth  in  a  court  of  law, 
a  witness  with  little  knowledge  and  little  mental  culti- 
vation, when  undertaking  to  give  an  account  of  simple 
occurrences  that  he  has  seen,  often  mingles  facts  and  con- 
jectures in  such  confusion,  that  the  lawyer  only  by  skillful 
cross-examination  and  a  careful  sifting  of  the  evidence 
can  make  the  witness  separate  the  facts  and  the  inferences 
(false  or  true)  which  he  has  drawn  from  these  facts. 


FALLACIES.  185 

Even  an  acute  and  well-trained  mind  is  not  always  free 
from  mistaking  an  inference  for  a  direct  perception.  An 
amusing  instance  of  this  is  related  of  Dr.  Wollaston,  a 
celebrated  English  chemist.  When  Sir  Humphry  Davy 
placed  in  his  hand  for  inspection  the  scientific  curiosity  of 
the  day,  a  bit  of  potassium,  a  substance  so  light  that  it 
will  float  on  water,  Dr.  Wollaston  carefully  examined  the 
potassium,  noted  its  metallic  lustre,  and  did  not  hesitate 
to  declare  it  a  metal.  In  this  philosopher's  mind  inti- 
mately associated  with  the  notion  of  metal  was  also  the 
notion  of  weight,  and  the  evidence  of  his  sense  of  touch 
was  insufficient  to  separate  the  two  ideas ;  so,  balancing 
the  specimen  on  the  tips  of  his  fingers,  he  exclaimed, 
"  How  heavy  it  is !  "  He  mistook  his  judgment  of  the 
weight  of  the  substance  for  the  sensation  itself. 

EXAMPLES. 

1.  The  length  of  the  seconds  pendulum  at  Greenwich  is  99.413cm;  find 
the  length  of  a  pendulum  which  makes  a  single  oscillation  in  1.5  seconds. 

2.  A  tuning-fork  makes  256  vibrations  per  second,  and  the  velocity  of 
sound  in  air  is  340m  per  second;  what  is  the  wave-length  of  the  note 
produced  ? 

Solution.  If  an  observer  be  at  a  distance  of  340m  from  the  fork, 
there  will  be,  between  the  fork  and  the  ear,  256  condensations  and  256 
rarefactions ;  but  a  condensation  and  a  rarefaction  make  up  a  wave ;  so 
there  will  be  256  waves  occupying  a  distance  of  340m,  hence,  if  in  340m 

340 

there  are  256  waves,  the  length  of  one  wave  will  be  —r^  =  1.33m. 

z5o 

3.  Find  the  wave-length  of  a  note  making  1000  vibrations  per  second, 
both  in  air  and  in  water ;  the  velocity  of  sound  in  air  being  1100  ft.  per 
second,  and  in  water  4900  ft.  per  second. 

4.  Taking  1120  ft.  per  second  as  the  velocity  of  sound  in  air,  find  the 
number  of  vibrations  which  a  tuning-fork,  vibrating  254  times  in  a 
second,  must  make  before  its  sound  is  audible  at  a  distance  of  144  ft. 


186  EXPERIMENTAL    PHYSICS. 

5.  A  stretched  string  10  ft.  long  is  in  unison  with  a  tuning-fork  mak- 
ing 256  vibrations  per  second ;  the  string  is  shortened  4  ft. ;  how  often 
will  it  now  vibrate  in  a  second  ? 

6.  A  string  is  fastened  at  one  end  to  a  peg  in  a  horizontal  board,  and 
the  other  end  passes  over  a  pulley  and  carries  16  pounds.     The  string 
thus  stretched  gives  the  note  C.     What  weight  must  be  put  in  place  of 
the  16  pounds,  so  that  the  string  shall  give  the  next  lower  octave  ? 

7.  Find  the  distance  of  an  obstacle  which  sends  back  the  echo  of  a 
sound  to  the  source  in  1.5  seconds,  when  the  velocity  of  sound  is  1100  ft. 
per  second. 

Solution.  In  1.5 seconds,  sound  travels  1100  X  |,  or  1650  ft.;  this  dis- 
tance the  sound  travels  in  going  to  the  obstacle  and  in  returning,  hence 
the  distance  of  the  obstacle  is  825  ft. 

8.  The  distance  from  the  top  of  a  well  to  the  surface  of  the  water  is 
210  ft.     What  time  will  elapse  between  producing  a  sound  at  its  mouth 
and  hearing  the  echo  ?     (Velocity  of  sound  =  1100  ft.  per  second.) 


CHAPTER   V. 

LIGHT. 

80.  Self-Lumiiious  Bodies ;    Non-Luminous  Bodies. 

When  we  are  in  a  place  exposed  to  either  the  sun  or  any 
other  glowing  body,  we  become  aware  of  the  existence  of 
objects  around  us.  If  the  place  be  securely  shielded  from 
the  sun,  or  if  the  glowing  substance  be  quenched,  then  by 
the  eye  we  perceive  nothing,  all  is  blank ;  but  when  the 
substance  is  kindled  again,  or  the  sun  shines  in  once  more, 
then  the  sight  again  perceives  the  objects  which  were  but 
a  moment  before  invisible.  This  mysterious  something 
that  is  necessary  to  render  objects  visible  is  called  light. 
Bodies  like  the  sun  or  a  lighted  lamp,  therefore,  have  the 
property  of  rendering  visible  not  only  themselves,  but 
also  the  objects  on  which  their  light  shines.  Bodies  which 
have  this  power  are  called  self-luminous  bodies.  On  the 
other  hand,  bodies  which  require  the  presence  of  a  self- 
luminous  body  to  enable  us  to  see  them  are  called  non- 
luminous  bodies. 

81.  Transparent,    Translucent,    and    Opaque    Sub- 
stances.   If,  in  a  lighted  room,  we  hold  a  piece  of  window- 
glass  before  the  eyes,  we  readily  see  the  objects  in  the  room 
through  the  glass.     Substances,  like  glass,  through  which 
objects  can  be  distinctly  seen  are  called  transparent.     Sub- 
stances, like  oiled  paper,  through  which,  though  light  pas- 
ses, objects  cannot  be  distinctly  seen,  are  called  translucent. 


188  EXPERIMENTAL    PHYSICS. 

Substances,  like  iron,  through  which  no  light  passes  are 
called  opaque. 

Make  a  list  of  four  transparent  substances,  another  of 
four  translucent  substances,  and  a  third  of  four  opaque 
substances. 

PHOTOMETRY. 

82.  Intensity  of  Illumination.  When  reading  a  book 
in  the  evening,  you  will  find  it  more  and  more  difficult  to 
see  the  letters  the  farther  the  book  is  carried  from  the 
lamp.  In  other  words,  on  carrying  a  book  from  the  lamp, 
the  degree  to  which  the  lamplight  illuminates  the  page  is 
diminished.  It  will  be  interesting,  as  an  introductory 
experiment  in  light,  to  find  the  relation  between  the 
degree  to  which  a  lamp  or  a  candle  illuminates  a  given 
object,  as  a  screen,  and  the  distance  of  the  object  from  the 
lamp.  In  the  course  of  the  experiment  we  shall  have 
occasion  to  use  the  term  intensity  of  illumination,  and 
it  is  important  to  understand  clearly  its  meaning,  so  we 
give  the  following  definition : 

Definition.  By  the  intensity  of  illumination  is  meant 
the  degree  to  which  a  source  of  light  supplies  a  given  body 
with  light. 

Experiment  82.  To  find  the  relation  between  the  inten- 
sity of  illumination  and  the  distance. 

Apparatus.  A  Letheby's  photometer;  five  candles.  Letheby's 
photometer  (Fig.  54),  an  instrument  for  measuring  the  intensity 
of  illumination,  is  constructed  as  follows:  there  is  a  long  bar  or  rod 
on  which  a  screen  of  paper,  stretched  on  a  frame,  is  placed  in  a 
vertical  position.  This  screen  has  a  translucent  spot  of  paraffine  on 


PHOTOMETRY.  189 

its  center.  Two  mirrors,  one  for  each  eye,  are  so  placed  that  an 
observer  may  see  both  sides  of  the  screen  at  the  same  time.  One  of 
the  lights  is  placed  on  one  side  of  the  screen  ;  the  other,  on  the  other 


FIG.  54. 

side.  The  mode  of  action  of  the  instrument  depends  on  the  fact 
that  when  a  piece  of  paper  having  a  paraffine  or  other  grease  spot 
on  it,  is  equally  illuminated  on  both  sides,  the  spot  becomes  nearly,  if 
not  quite,  invisible. 

Oirectioiis.  This  experiment  is  to  be  performed  in 
a  darkened  room.  Place  in  line  four  candles,  all  of  the 
same  height,  on  one  of  the  sliding  blocks,  in  such  a  way 
that  the  line  of  candles  is  at  right  angles  to  the  bar.  On  the 
other  side  of  the  screen  place  on  a  sliding  block  the  other 
candle.  Light  the  candles  and  trim  the  wicks  so  that  the 
flames  shall  be  of  equal  size.  In  order  to  let  the  candles 
get  well  burning,  it  is  best  to  wait  a  few  minutes  before 
making  any  measurements.  When  trimming  the  candles, 
look  at  them  not  with  the  naked  eye,  but  through  col- 
ored glasses ;  otherwise  the  eye  will  not  be  as  sensitive  to 
the  difference  of  light  and  shade  on  the  screen.  Slide 
the  block  carrying  the  four  candles  along  the  bar  till  the 
middle  of  the  line  of  flames  is  at  a  distance  of  80cm  from 
the  screen.  By  sliding  the  single  candle  back  and  forth 
along  the  bar,  find  a  position  for  it  such  that  the  spot 
shall  disappear  as  you  look  into  the  mirrors  (or,  if  the  spot 
cannot  be  made  to  vanish  entirely,  get  the  two  images  of 


190  EXPERIMENTAL    PHYSICS. 

the  spot,  as  seen  in  the  mirrors,  of  the  same  shade). 
Record  the  distance  of  the  four  candles  from  the  screen ; 
also  the  distance  from  the  screen  of  the  single  candle 
when  placed  in  the  position  you  have  been  directed  to  find. 

Next  put  the  four  candles  at  a  distance  of  160cm  from 
the  screen,  and  find  the  corresponding  position  of  the 
single  candle.  As  before,  record  the  distances. 

Assuming  that  each  of  the  five  candles  gives  out  the 
same  amount  of  light,  how  does  the  amount  of  light  given 
out  by  the  four  candles  compare  with  that  given  by  the 
single  candle? 

In  each  case,  how  does  the  distance  of  the  four  candles 
compare  with  that  of  the  single  one  ? 

In  this  experiment  the  intensity  of  illumination  on  the 
screen  due  to  the  single  candle  was  equal  to  the  intensity 
of  illumination  due  to  the  group  of  four  candles  placed  at 
a  greater  distance  from  the  screen  on  the  other  side.  Now 
consider  that  from  the  group  of  four  candles,  when  the 
distance  has  been  properly  adjusted,  three  are  removed,  so 
as  to  leave  only  one  candle ;  how  much  light  falls  upon 
the  screen  from  this  single  candle  as  compared  with  the 
amount  of  light  from  the  group  of  four  ? 

Divide  the  greater  distance  (the  distance  of  the  four 
candles  from  the  screen)  by  the  lesser  distance  (the  dis- 
tance of  the  single  candle  on  the  other  side  of  the  screen); 
also  divide  the  intensity  of  illumination  of  the  single 
candle  by  the  intensity  of  illumination  of  a  single  candle 
supposed  to  be  placed  at  a  distance  from  the  screen  equal 
to  that  of  the  group  of  four  candles. 

If  the  two  quotients  are  not  equal,  try  to  make  them 
equal  by  squaring  or  cubing  one  of  them. 


PHOTOMETRY.  191 

What  relation  should  you  infer  holds  between  the  dis- 
tance of  a  light  from  a  screen  and  the  intensity  ^  of  its 
illumination  ? 

QUESTIONS.  How  would  the  distances  compare  if  9  candles  were  used 
in  place  of  the  4  ?  If  16  candles  were  used  ?  If  25  candles  were  used  ? 

Experiment  83.  To  find  how  many  candles  will  give 
the  same  intensity  of  illumination  as  a  kerosene  lamp. 

Apparatus.  A  Letheby's  photometer  ;  a  kerosene  lamp  with  a 
chimney ;  a  candle. 

Directions.  At  a  distance  of  50cm  on  one  side  of  the 
screen  place  the  candle.  On  the  other  side  of  the  screen 
place  the  well-trimmed  lamp  with  its  flame  turned  flatwise 
towards  the  screen.  Light  the  candle  and  wait  till  it  is 
burning  well.  See  that  the  lamp-flame  and  the  candle- 
flame  are  at  equal  distances  above  the  table.  Move  the 
lamp  till  the  spot  disappears  or  till  both  images  are  of  the 
same  shade.  Measure  and  record  the  distances. 

Denote  the  power  of  the  candle  by  1,  and  that  of  the 
lamp  by  x,  then  by  the  law  brought  out  in  the  preceding 
experiment : 

—  =  intensity  of  illumination  of 
(distance  of  the  candle)2 

the  candle. 


-  =  intensity  of  illumination  of 


(distance  of  the   lamp) 2 
the  lamp. 

But  in  the  present  experiment  you  have  adjusted  the 
distances  in  such  a  way  as  to  make  the  intensity  of  illumi- 
nation of  the  candle  on  the  screen  equal  to  that  of  the 
lamp,  hence, 


192  EXPERIMENTAL   PHYSICS. 


(distance  of  the  lamp) 2       (distance  of  the  candle) 2 
_  /  distance  of  the  lamp  \2 
\distance  of  the  candle/ 

Making  use  of  this   relation,  compute  the  number  of 
candles  to  which  the  lamp  is  equivalent. 

Definition.      Photometry   is   the   art  of  measuring    the 
intensity  of  light. 


RAYS. 

Experiment  84.  To  find  whether  light  passes  through 
the  air  in  straight  lines. 

Apparatus.  A  Bunsen  burner  arranged  to  give  the  luminous 
flame ;  three  pieces  of  cardboard. 

Directions.  Set  up  the  three  cards,  through  each  of 
which  a  pin-hole  has  been  made,  in  such  a  way  that  the 
flame  or  a  portion  of  it  can  be  seen  through  the  holes. 

When  the  flame  can  be  seen,  are  the  three  holes  in  the 
same  straight  line  ? 

Does,  then,  light  pass  through  the  air  in  straight  lines  ? 

83.  Kay ;  Beam  ;  Pencil.  A  single  ray,  or  line,  of 
light  (Fig.  55, 1)  is  represented  by  a  straight  line.  A  beam 
of  light,  that  is,  a  bundle  of  parallel  rays  (Fig.  55,  2),  is 
represented  by  several  parallel  straight  lines.  A  pencil 
of  light,  that  is,  a  group  of  rays  converging  to  or  diverging 
from  a  point,  is  represented  by  a  group  of  converging  or 
by  a  group  of  diverging  lines.  Fig.  55,  3,  represents  a 
converging  pencil  in  which  the  rays  proceeding  from  some 


SHADOWS.  193 

source  of  light  on  the  left  draw  nearer  together,  so  as  to 
cross  each  other  at  the  point  0.     Fig.  55,  4,  represents  a 


FIG.  55. 

diverging  pencil  in  which  the  rays  proceeding  from  the 
source  of  light  0'  spread  away  from  each  other  as  they  pro- 
ceed to  the  right. 

SHADOWS. 

Experiment  85.      To  find  the  cause  of  a  shadow. 

Apparatus.  An  opaque  cylinder  8cm  or  10cm  in  diameter;  two 
candles ;  a  piece  of  cardboard  about  20cm  square. 

Directions.  This  experiment  is  to  be  performed  in  a 
darkened  room.  Place  the  cylinder  on  a  table.  Put  the 
two  lighted  candles  on  the  table  at  a  distance  of  10cm  or 
12cm  from  the  cylinder,  making  the  distance  between  the 
candles  equal  to  the  diameter  of  the  cylinder.  On  the 
other  side  of  the  cylinder  and  about  10cm  from  it  support 
the  piece  of  cardboard  in  a  vertical  position.  Notice  a 
black  band  bordered  by  two  lighter  ones  on  the  cardboard. 
With  a  pin  pierce  a  hole  through  the  screen  where  the 
black  band  crosses.  Look  through  this  hole  towards  the 
lights. 


194  EXPERIMENTAL   PHYSICS. 

Do  you  see  either  or  both  of  the  candles  ? 

Pierce  a  hole  through  the  screen  where  one  of  the 
lighter  bands  crosses.  Through  the  hole  thus  made  look 
towards  the  candles. 

Can  you  see  either  candle  ? 

Pierce  a  hole  through  the  other  lighter  band. 

Looking  through  this  hole,  which  candle  can  you  see? 

Move  the  screen  back  and  forth  to  see  how  the  widths 
of  the  bands  change. 

As  you  move  the  screen  away,  what  change  is  there  in 
the  width  of  the  black  band  ? 

Pierce  a  hole  through  a  brightly  lighted  part  of  the 
screen. 

Looking  through  this  hole,  can  you  see  more  than  one 
candle  ? 

The  black  part  of  the  shadow  is  called  the  umbra ;  the 
border  is  called  the  penumbra. 

From  your  observations  explain  the  formation  of  a 
shadow,  accounting  for  the  umbra  and  the  penumbra. 

Does  the  shadow  extend  from  the  cylinder  to  the  screen  ? 

IMAGES. 

84.  Formation  of  Images  by  Means  of  Small  Aper- 
tures. If  a  hole  is  made  in  the  shutter  of  a  dark  room, 
an  inverted  picture  of  the  scene  outside  in  front  of  the 
window  appears  on  the  wall  of  the  room  opposite  the 
shutter.  When  sunlight  passes  through  the  spaces  between 
the  leaves  of  trees,  circular  patches  of  light  are  seen  on 
the  ground ;  if,  however,  the  sun  should  be  partly  eclipsed, 
the  patches  of  light  would  be  crescent-shaped.  The  object 


IMAGES.  195 

of  the  following  experiment  will  be  to  study  the  formation 
of  images  obtained  when  light  passes  through  small  aper- 
tures, like  the  hole  in  the  shutter  or  the  small  spaces 
between  the  leaves  of  trees. 

Experiment  86.  To  find  an  explanation  of  the  forma- 
tion of  an  image  (picture)  on  the  screen  of  a  pin-hole  camera. 

Apparatus.  A  pin-hole  camera,  which  consists  of  a  box  about 
10cm  in  width  and  depth,  and  30cm  long,  with  one  end  closed  and  the 
other  open.  In  the  open  end  a  frame,  carrying  a  translucent  screen, 
slides.  In  the  center  of  the  closed  end  is  cut  a  rather  large  hole, 
which  is  covered  by  a  piece  of  thin  sheet  brass,  through  which  a 
small  hole  is  pierced. 

Directions.  •  Slide  the  screen  into  the  box,  hold  the 
brass-covered  end  towards  a  bright  gas-flame  in  a  darkened 
room,  and  look  into  the  open  end  of  the  box  towards  the 
flame.  At  first  have  the  box  near  the  flame,  then  gradu- 
ally take  it  farther  away,  always  looking  in,  through  the 
open  end,  at  the  picture  on  the  screen.  Also  slide  the 
screen  back  and  forth. 

Can  you  get  a  position  of  the  screen  such  that  the  image 
of  the  flame  is  very  distinct? 

Explain,  by  a  drawing,  why  the  image  (picture)  is 
inverted.  (See  your  inference  from  Exp.  84.) 

QUESTIONS.  Why  are  circular  patches  of  light  seen  on  the  ground 
beneath  the  trees  in  summer  when  the  sun  is  shining  ?  When  the  sun  is 
partly  eclipsed,  why  are  these  patches  crescent-shaped  ? 

REFLECTION. 

85.  Reflection  of  Light ;  Angle  of  Incidence ;  Angle 
of  Reflection.  If  the  eye  is  in  a  proper  position  when 
sunlight  falls  upon  a  suitable  surface,  the  calm  surface  of 


196 


EXPERIMENTAL    PHYSICS. 


a  lake  for  example,  the  image  of  the  sun  can  be  seen  in 
the  lake.  The  rays  of  light  from  the  sun  strike  the  sur- 
face of  the  water,  and  some  of  them  are  bent  back  from 
the  surface  and  so  reach  the  eye.  This  bending  back  of 
the  rays  is  called  reflection.  The  rays  that  strike  the  sur- 
face are. called  incident  rays  (Latin  incidere,  to  fall  upon). 
The  rays  that  are  bent  back  from  the  surface  are  called 
reflected  rays  (Latin  reflectere,  to  bend  back). 

If  a  perpendicular  be  erected  to  the  reflecting  surface, 
the  surface  of  the  lake  in  this  case  at  a  point  where  an 
incident  ray  falls  upon  it,  the  angle  between  the  perpendic- 
ular and  the  incident  ray  is  called  the  angle  of  incidence  ,* 
the  angle  between  the  perpendicular  and  the  reflected  ray 
is  called  the  angle  of  reflection  (Fig.  56). 


B 


c 

FIG.  56. 

AS,  reflecting  surface  ;   CD,  perpendicular  (in  optics,  often  called  a  normal) ;  EC, 
incident  ray;  Cf,  reflected  ray;  ECD,  angle  of  incidence  ;  DCF,  angle  of  reflection. 

Experiment  87.  To  find  whether  there  is  any  simple 
relation  between  the  angle  of  incidence  and  the  angle  oj 
reflection. 

Apparatus.  A  small  plane  mirror ;  a  sheet  of  paper  50 cm  square  ; 
a  meter  stick ;  a  pin  ;  a  protractor  ;  two  rubber  bands ;  a  block. 


REFLECTION.  197 

Directions.  By  means  of  tacks  at  the  corners,  fasten 
the  sheet  of  paper  to  the  table.  From  the  middle  point 
of  one  side  of  the  paper  draw  a  straight  line  to  the  middle 
point  of  the  opposite  side.  Fasten  the  mirror  to  a  rectang- 
ular block,  by  means  of  two  small  rubber  bands,  so  that  the 
back  of  the  mirror  rests  against  one  of  the  narrow  sides  of 
the  block.  Place  the  mirror  thus  arranged  with  its  edge 
along  the  middle 
portion  of  this 
straight  line 
Have  the  silvered 
part  of  the  mir- 
ror over  the  line. 
The  reflection 
takes  place  at  the 
silvered  surface. 

At  some  distance 

,.  *    ii  FIG.  57. 

in    front    of    the 

mirror,  but  to  one  side  of  its  center,  stick  a  pin  upright  in 
the  paper.  On  the  paper  lay  the  meter  stick  (Fig.  57)  in 
such  a  position  that  its  direction  makes  an  acute  angle 
with  the  face  of  the  mirror.  By  sighting  along  the  edge 
of  the  meter  stick,  point  it  towards  the  image  of  the  pin 
formed  in  the  mirror.  When  the  meter  stick  has  been 
carefully  adjusted  so  as  to  point  accurately  towards  the 
image,  and  at  the  same  time  to  make  an  acute  angle  with 
the  face  of  the  mirror,  draw,  with  a  sharp  pencil,  a  line  on 
the  paper  along  the  edge  of  the  meter  stick  to  meet  the 
mirror.  Remove  the  mirror,  and  produce  this  line  until  it 
meets  the  line  drawn  across  the  paper.  Draw  a  straight 
line  connecting  the  point  of  meeting  of  the  two  lines  with 


198  EXPERIMENTAL    PHYSICS. 

the  pin.  At  the  point  of  intersection  of  the  three  lines 
erect  a  perpendicular  to  the  line  drawn  across  the  paper. 

If  the  mirror  were  still  in  position,  would  the  line  last 
drawn  be  perpendicular  to  the  surface  of  the  mirror? 

With  the  protractor,  measure  the  angles  formed  by  the 
oblique  lines  with  the  perpendicular.  The  angle  formed 
with  the  perpendicular  by  the  line  from  the  pin  is  the 
angle  of  incidence,  and  the  angle  formed  with  the  perpen- 
dicular by  the  line  from  the  mirror  to  the  eye  (found  by 
sighting  along  the  meter  stick)  is  the  angle  of  reflection. 

After  measuring  these  angles  with  the  protractor,  can 
you  infer  a  relation  between  the  two  angles  ? 

If  you  have  performed  the  experiment  accurately,  your 
answer  to  the  question  is  the  statement  of  the  chief  law 
of  the  reflection  of  light. 

Make  as  brief  a  statement  of  the  law  as  possible. 

Preserve  the  paper  and  paste  it  into  your  note-book. 

PLANE   MIRRORS. 

86.  Images  in  a  Plane  Mirror.  When  you  see  your 
image,  or  reflection,  as  it  is  sometimes  called,  in  a  mirror, 
doubtless  you  have  noticed  that  it  appears  behind  the 
mirror ;  that  when  you  move,  the  image  moves.  It  will 
be  the  object  of  the  two  following  experiments  to  find  a 
relation  between  the  distance  of  the  object  from  the  mirror 
in  front  and  the  apparent  distance  of  the  image  behind  the 
mirror ;  also  something  about  the  relative  size  and  shape 
of  image  and  object. 

Experiment  88.  To  find  what  relation  holds  between  the 
position  of  the  image  of  a  point  and  the  position  of  the  point. 


PLANE   MIRRORS.  199 

Apparatus.  The  same  as  in  the  last  experiment,  with  a  fresh 
sheet  of  paper. 

Directions.  As  in  the  preceding  experiment,  fasten 
the  sheet  of  paper  to  the  table,  draw  a  straight  line  across 
the  sheet,  and  place  the  mirror  and  the  pin  in  position. 
Then  lay  the  meter  stick  on  the  paper,  and  by  sighting 
along  its  edge,  which  should  be  inclined  at  an  acute  angle 
to  the  face  of  the  mirror,  point  it  directly  towards  the 
image  of  the  pin  (the  pin  is  so  small  that  we  shall  consider 
its  position  as  a  mere  point).  With  a  sharp  lead  pencil, 
guided  by  the  edge  of  the  meter  stick,  draw  a  line  on  the 
surface  of  the  paper  directly  towards  the  image.  Without 
disturbing  either  the  pin  or  the  mirror,  sight  at  the  image 
of  the  pin  from  an  entirely  different  direction,  having  this 
new  direction  make  as  large  an  angle  as  practicable  with 
the  former  line  along  which  you  sighted,  and  as  before 
draw  a  line  towards  the  image.  Now  remove  the  mir- 
ror, and  carefully  produce  the  two  lines  you  have  drawn 
towards  the  mirror  until  they  cross  each  other.  Also  from 
the  pin  draw  a  line  at  right  angles  to  the  line  that  the 
mirror  rested  on,  and  continue  it  till  it  crosses  the  other 
two  lines. 

Now  replace  the  mirror  in  its  old  position,  change  the 
position  of  the  pin,  and  make  a  new  set  of  observations. 
Finally,  put  the  pin  in  another  position  and  make  another 
set  of  observations. 

Remembering  that  the  pin  is  the  object,  and  that  its 
reflection  in  the  mirror  is  the  image,  study  the  results  of 
your  experiment  with  a  view  to  answering  the  following 
questions  : 

How  far  behind  the  mirror  does  the  image  appear  to  be 


200  EXPERIMENTAL   PHYSICS. 

as  compared  with  the  distance  of  the  object  in  front  of  the 
mirror  ? 

For  a  given  position  of  the  object,  does  the  image  always 
appear  at  the  same  place,  no  matter  from  what  direction 
you  look  into  the  mirror? 

If  a  line  is  drawn  from  the  object  to  the  image,  is  this 
line  perpendicular  to  the  mirror? 

Paste  the  paper  into  your  note-book. 

Experiment  89.  To  find  the  relation  between  the  size 
and  position  of  an  object  and  its  imaye. 

Apparatus.  The  same  as  that  of  the  preceding  experiment,  together 
with  two  pins  and  a  fresh  sheet  of  paper. 

IMrections.  Fasten  the  paper  to  the  table,  draw  a  line 
across  it,  and  on  this  line  stand  the  mirror.  At  a  distance 

of  a  few  centi- 
meters in  front  of 
the  mirror  draw 
on  the  paper  a 
triangle  (Fig.  58) 
whose  sides  are 
respectively  6cm, 
8cm,  and  10cm  long. 
By  sticking  three 
pins  upright  in  the 

paper,  mark  the  angles  of  the  triangle.  By  the  method 
of  sighting  used  in  the  preceding  experiment,  find  the 
position  of  the  image  of  each  of  these  pins ;  that  is,  find 
the  positions  of  the  angles  in  the  image  of  the  triangle. 
Connect  by  straight  lines  the  points  thus  found. 


PLANE    MIRKOKS.  201 

How  does  the  size  of  the  image  compare  with  that  of 
the  object? 

How  does  the  distance  from  the  mirror  of  any  point  in 
the  image  compare  with  the  distance  from  the  mirror  of 
the  corresponding  point  of  the  object? 

As  compared  with  the  object,  is  the  image  inverted, 
that  is,  turned  upside  down? 

SUGGESTION.  Call  to  mind  the  images  of  the  pins,  whether  they  were 
inverted  or  upright. 

Is  the  image  laterally  inverted,  that  is,  is  the  right-hand 
side  of  the  object  opposite  its  own  reflection  ? 

Paste  into  your  note-book  the  sheet  on  which  the 
triangle  is  drawn. 

Knowing  that  a  real  image  can  be  caught  on  a  screen, 
and  that  a  virtual  image  cannot  be  caught  on  a  screen^ 
answer  the  following  questions : 

Is  the  image  seen  when  looking  into  an  ordinary 
looking-glass  real  or  virtual? 

What  kind  of  image  was  formed  in  Exp.  86  ? 

87.  Multiple  Reflections.  When,  after  reflection  at 
the  surface  of  a  plane  mirror,  a  ray  of  light  falls  upon  a 
second  plane  mirror,  the  ray  is  reflected  from  this  second 
mirror  in  such  a  way  as  to  make  the  angle  of  incidence 
equal  to  the  angle  of  reflection.  The  result  of  the  reflec- 
tions of  light  from  one  plane  mirror  to  another  is  a 
number  of  images,  the  number  depending  upon  the  angle 
which  the  two  mirrors  make  with  each  other.  The  object 
of  the  next  experiment  will  be  to  find  the  number  of 
images  formed  when  two  mirrors  are  placed  at  different 
angles  with  each  other. 


202  EXPERIMENTAL    PHYSICS. 

Experiment  9O.  To  find  the  number  of  images  formed 
ly  two  plane  mirrors,  when  making  with  each  other  (a)  an 
angle  of  90°,  (b)  an  angle  of  60°,  (c)  an  angle  of  40°. 

Apparatus.  Two  plane  mirrors  ;  two  rectangular  blocks  of  wood  ; 
four  rubber  bands  ;  a  sheet  of  paper  50cm  square  ;  a  protractor ;  a  pin. 

Directions.  Fasten  the  paper  to  the  table.  By  means 
of  the  rubber  bands  fasten  the  mirrors  to  the  blocks.  With 
a  sharp  lead-pencil  draw  on  the  paper  near  the  center  two 
straight  lines  crossing  each  other  at  right  angles,  that  is,  90°. 

Place  the  two  mirrors  (Fig.  59)  in  such  a  position  that  a 
long  edge  of  one  shall  lie  along  one  of  these  lines,  a  long 


FIG.  59. 


edge  of  the  other  mirror  along  the  other  straight  line,  thus 
making  the  angle  formed  by  the  planes  of  the  mirrors  a 
right  angle.  At  a  distance  of-  about  4cm  from  the  place 
where  the  mirrors  meet,  stick  a  pin  upright  in  the  paper 
lying  between  the  mirrors.  Record  the  number  of  images 
of  the  pin. 

Now  by  the  aid  of  the  protractor  make  the  angle 
between  the  two  mirrors  60°.  To  do  this,  draw  a  line  on 
the  paper,  and  then  measure  off  with  the  protractor  an 
angle  of  60°  from  this  line,  and  then  draw  a  second  line, 


PLANE    MIRRORS.  203 

making  an  angle  of  60°  with  the  first ;  the  mirrors  can 
now  be  placed  on  these  lines  so  as  to  make  an  angle  of 
60°  with  each  other.  Stick  the  pin  into  the  paper  as 
before,  and  count  the  number  of  its  images.  Record  the 
number  of  images. 

Finally,  place  the  mirrors  at  an  angle  of  40°  to  each 
other.  Record  the  number  of  images. 

Experiment  91.  To  find  whether  the  multiple  images 
formed  by  two  plane  mirrors  lie  on  a  circumference  of  which 
the  intersection  of  the  lines  on  which  the  mirrors  stand  is  the 
center. 

Apparatus.  The  same  as  in  the  last  experiment,  together  with  a 
long  pin. 

Directions.  Fasten  the  paper  to  the  table ;  draw  on  it 
two  lines  at  60°  to  each  other.  Stick  the  little  pin  into 
the  portion  of  the  paper  lying  between  the  two  mirrors, 
which  should  have  been  placed  in  position  on  the  two 
lines.  With  the  long  pin  locate  the  position  of  each 
of  the  images.  These  images  appear  to  occupy  positions 
behind  the  mirrors  ;  by  moving  the  long  pin  behind  the 
mirrors  this  pin  can  be  made  to  coincide  with  the  position 
of  each  of  the  images.  This  position  is  secured  when  on 
moving  the  eye  from  side  to  side  in  front  of  the  mirror  the 
image  and  the  long  pin  always  occupy  the  same  position. 
Mark  each  of  these  positions.  Mark  also  the  position  of 
the  object,  that  is,  the  pin  stuck  into  the  paper  between 
the  mirrors.  Now  clear  the  paper,  and  with  the  inter- 
section of  the  two  lines,  the  point  over  which  the  narrow 
edges  of  the  mirrors  came  together,  as  a  center,  and  a 


204  EXPERIMENTAL    PHYSICS. 

radius  equal  to  the  distance  of  the  object  from  the  inter- 
section of  the  two  lines,  describe  a  circumference. 

Through  what  points,  previously  marked  on  the  paper, 
does  the  circumference  pass  ? 

What  inference  can  you  draw  from  this  experiment  ? 

88.  Dependence  of  the  Number  of  Images  on  the 
Angle  between  Two  Plane  Mirrors.     The  relation  that 
exists  between  the  angle  formed  by  two  plane  mirrors  and 
the  number  of  images  of  an  object  formed  by  the  mirrors 
is  as  follows : 

Provided  the  number  of  degrees  contained  in  the  angle 
between  the  two  mirrors  will  divide  without  a  remainder 
360,  the  number  of  degrees  in  a  circumference,  the  num- 
ber of  images  formed  will  always  be  one  less  than  the 
value  of  the  quotient  thus  obtained. 

Turn  back  to  your  record  of  Exp.  90,  and  compare  the 
number  of  images  obtained  in  each  case  with  the  number 
computed  in  accordance  with  the  foregoing  statement. 

89.  The  Kaleidoscope.     The  fact  that  two  plane  mir- 
rors placed  at  an  angle  of  60°  to  each  other  will  form 
five  images  of  an  object,  these  images  being  arranged  sym- 
metrically with  respect  to   the   mirrors,  has  led  to  the 
construction  of  the  kaleidoscope,  which  in  its  simplest  form 
consists  of  two  long,  narrow,  plane  mirrors  making  an 
angle  of  60°  with  each  other.     These  mirrors  are  con- 
tained  in  a  tube,  closed  at  one   end   by  a   glass   plate 
covered  by  a  diaphragm  with  an  aperture  in  its  center;  at 
the  other  end  by  a  plate  of  ground  glass,  on  the  inner 
side  of  which  lie  loose  fragments  of  colored  glass.     On 
looking  through  the  aperture  and  along  the  axis  of  the 
tube,  an  observer  sees  a  design,  symmetrical  about  the 


CYLINDRICAL    MIRRORS.  205 

axis  and  often  very  beautiful,  formed  by  the  fragments 
of  colored  glass  and  their  five  reflections.  Whenever  the 
tube  is  shaken,  the  arrangement  of  the  fragments  on  the 
ground  glass  is  changed,  and  a  new  design  appears. 


EXAMPLES. 

1.  When  the  distance  of  a  gas  flame  was  84cm  from  the  grease  spot  of 
a  photometer,  and  that  of  a  candle  40cn)  on  the  other  side,  the  grease  spot 
disappeared.     To  how  many  candles  is  the  gas  flame  equivalent  ? 

2.  An  incandescent  lamp  equivalent  to  10  candles  is  placed  at  a  dis- 
tance of  lm  from  a  screen.     At- what  distance  from  the  screen  must  a 
candle  be  placed  in  order  to  give  the  same  intensity  of  illumination  ? 

3.  An  object  is  placed  at  a  distance  of  4cm  in  front  of  a  plane  mirror. 
How  far  from  the  object  will  the  image  appear  ? 

4.  How  many  images  of  an  object  will  be  formed  by  two  plane  mir- 
rors, if  they  make  an  angle  with  each  other  of  18°  ?    If  they  make  an 
angle  of  10°  ?     If  they  are  parallel  ? 

5.  The  aperture  of  a  pin-hole  camera  is  circular  in  shape,  that  of 
another  is  triangular,  while  that  of  a  third  is  square.     What  effect  has 
the  shape  of  the  aperture  upon  the  image  formed  on  the  screen  of  the 
camera  ? 

6.  If  a  candle  is  placed  at  a  distance  of  30cm  from  an  opaque  body 
12cm  wide,  what  will  be  the  width  of  the  shadow  cast  by  the  opaque  body 
when  the  shadow  falls  upon  a  screen  100cm  distant  from  the  candle  ? 


CYLINDRICAL    MIRRORS. 

9O.    Convex  and  Concave  Cylindrical  Mirrors.      The 

polished  outside  surface  of  a  cylindrical  calorimeter,  such 
as  was  used  in  some  of  the  experiments  in  heat,  is  a  con- 
vex cylindrical  mirror,  while  the  inner  surface,  if  polished, 
is  a  concave  cylindrical  mirror.  The  cylindrical  mirrors 
usually  met  with  are  segments  formed  by  cutting  from 
a  cylindrical  surface  strips  running  lengthwise  of  the  sur- 


206  EXPERIMENTAL   PHYSICS. 

face.  The  center  of  curvature  of  a  cylindrical  mirror  is 
the  center  of  the  circle  of  which  the  portion  of  the  mirror 
under  consideration  is  the  arc. 

On  looking  into  a  cylindrical  mirror,  you  will  see  a 
distorted  image :  when  the  mirror  is  held  in  a  vertical 
position,  the  image  has  one  form,  but  when  the  mirror 
is  held  in  a  liorizontal  position,  the  image  assumes  a 
different  form.  It  will  be  the  object  of  the  next  two 
experiments  to  make  you  acquainted  with  the  laws  of 
cylindrical  mirrors,  and  so  to  help  you  to  understand 
better  the  reason  for  the  formation  of  the  curious  images 
which  cylindrical  mirrors  give. 

Experiment  92.  To  find  how  the  image  in  a  convex 
cylindrical  mirror  compares  with  the  object  in  position,  size, 
and  shape. 

Apparatus.  A  convex  cylindrical  mirror  mounted  on  a  semi- 
circular support  of  wood;  a  small  sheet  of  paper;  a  small  pin; 
a  meter  stick. 

Directions.  Lay  the  sheet  of  paper  flat  upon  a  table, 
and  upon  this  sheet  put  the  mirror  (Fig.  60).  With  a 
sharp-pointed  lead  pencil  draw  a  line  round  the  support. 
Draw  on  the  paper,  at  a  distance  of  about  5cm  from  the 
front  of  the  mirror,  a  straight  line  about  6cm  long,  and 
mark  the  ends  and  the  center  of  this  line  with  numbers. 
We  shall  call  this  line  the  object.  Stick  the  pin  upright 
into  one  extremity  of  the  line.  In  order  to  get  the  posi- 
tion of  the  image  of  the  pin,  sight  at  the  image  along  the 
edge  of  a  meter  stick  laid  on  the  table,  and,  guided  by 
the  edge  of  the  meter  stick,  draw  a  line  towards  this 
image ;  then  move  the  meter  stick  to  a  place  widely  dif- 


CYLINDRICAL    MIRRORS.  207 

ferent  from  the  first,  sight  along  the  meter  slick  at  the 
image,  and  towards  it  draw  another  line.     Each  of  the 
lines   just   drawn   should   be    numbered   with   the   same 
figure  as  that  which  num- 
bers the  point   into  which 
the  pin  was   stuck.      Now 
stick  the  pin  into  the  mid- 
dle point,  sight  at  its  image, 
and,  as  before,  draw  lines, 
and  number  each  with  the 
same  figure  with  which  you 
numbered  the  middle  point. 
Finally,  stick  the   pin  into 
the  other  extremity  of  the 
line,  and  again  sight  at  its  image,  and  draw  lines. 

Remove  the  mirror  from  the  paper,  and  get  the  position 
of  each  of  the  three  images  by  producing  each  pair  of 
lines  till  they  cross.  Connect  by  a  line  the  three  points 
thus  found.  This  line  is  the  image. 

Is  the  image  as  far  behind  the  mirror  as  the  object  is  in 
front? 

Is  the  size  of  the  image  larger  or  smaller  than  that  of 
the  object? 

Is  the  shape  of  the  image  the  same  as  that  of  the  object  ? 

Make  a  dot  at  the  middle  of  the  straight  line  forming 
one  side  of  the  outline  of  the  support.  This  dot  will 
mark  the  center  of  curvature  of  the  mirror.  Join  by 
lines  the  center  of  curvature  to  each  of  the  points  of  the 
line  into  which  the  pin  was  stuck. 

Does  each  of  these  lines  pass  through,  or  nearly  through, 
the  corresponding  points  of  the  image  ? 


208  EXPERIMENTAL    PHYSICS. 

Repeat  the  experiment  on  a  fresh  sheet  of  paper  with  a 
line  5cm  long  drawn  6cm  from  the  face  of  the  mirror. 

From  the  results  which  you  now  obtain,  do  you  get  the 
same  answers  to  the  questions  as  before  ? 

Did  the  height  of  the  image  seem  to  be  the  same  as  the 
height  of  the  pin  ?  Did  the  width  of  the  image  seem  to 
be  the  same  as  that  of  the  pin? 

Hence,  should  you  say  that  the  lines  of  an  object,  which 
are  parallel  to  the  vertical  lines  of  a  convex  cylindrical 
mirror,  appear  in  the  image  unchanged  in  length,  while 
horizontal  lines  in  the  object  are  shortened  in  the  image  ? 

91.  Distance  of  Image  from  Convex  Cylindrical 
Mirror.  The  law  that  the  angle  of  reflection  equals  the 


FIG.  61. 


angle  of  incidence — a  law  which  holds  true  for  both  curved 
and  plane  mirrors  —  will  enable  the  student  to  see,  as  is 
indicated  in  Fig.  61,  that  the  image  of  a  point  is  not,  as 
in  the  case  of  plane  mirrors,  so  far  behind  a  convex  mir- 
ror as  the  point  is  in  front,  but  that  the  image  is  at  a  less 
distance  from  the  mirror  than  is  the  point  itself. 

The  arc  LM  represents  the  mirror.  Let  0  be  the  posi- 
tion of  the  object.  Let  OL  and  OM  be  two  rays  from  0 
meeting  the  mirror  in  L  and  M.  From  (7,  the  center  of 


CYLINDRICAL    MIRRORS.  209 

curvature,  are  drawn  the  radii  CL  and  CM,  which  are  pro- 
duced to  D  and  F.  The  reflected  rays  L  G-  and  MK  are 
drawn  so  as  to  make  the  angles  GrLD  and  KMF  equal 
respectively  to  the  angles  OLD  and  OMF,  as  the  angle  of 
reflection  is  equal  to  the  angle  of  incidence.  When  the  lines 
CrL  and  KM  are  produced,  they  meet  in  the  point  /,  and 
this  point  gives  the  position  of  the  image  of  the  object  at  0. 
In  the  same  way  the  object  at  0'  will  have  its  image 
formed  at  I'.  The  image  is  nearer  the  mirror  than  is  the 
object. 

92.    Images  formed  by  a  Concave  Cylindrical  Mirror. 

All  images  formed  by  a  convex  cylindrical  mirror  or  by  a 
plane  mirror  are 
virtual.  But 
with  a  concave 
cylindrical  mir-  /^ 
ror,  both  virtual 
images  and  real 
images  can  be 
formed.  Wheth- 
er the  image  formed  by  a  concave  cylindrical  mirror  will 
be  real  or  virtual  depends  upon  the  distance  of  the  object 
in  front  of  the  mirror,  as  indicated  by  the  following  con- 
struction : 

In  Fig.  62  the  arc  LM  represents  the  mirror.  Let  0  be 
the  position  of  the  object.  Let  OL  and  OM  be  two  rays  from 
0  meeting  the  mirror  in  L  and  M.  From  (7,  the  center  of 
curvature,  are  drawn  the  radii  CL  and  CM.  The  reflected 
rays  LGr  and  MK  are  drawn  so  as  to  make  the  angles 
GrLO  and  KMC  equal  respectively  to  the  angles  OLC 
and  OMC,  as  the  angle  of  reflection  is  equal  to  the  angle 


210  EXPERIMENTAL   PHYSICS. 

of  incidence.     When  the  lines  G-L  and  .Of  are  produced, 

they  meet  in  the  point  J,  and  this  point  gives  the  position 

of  the  image  of  the  object  at  0. 

If  the  object  is  at  the  point  0',  the  reflected  rays  will 

actually  cross  at  /'  in  front  of  the  mirror.     It  is  to  be 

noted  that  the 
point  0  is  at  a 
distance  from 
the  mirror  less 
than  half  the 
radius  of  curva- 
ture, while  the 
point  0'  is  at  a 

distance  greater  than  half  the  radius  of  curvature.     The 

image  of  an  object  at  0  is  virtual,  while  that  of  an  object 

at  0'  is  real. 

Experiment  93.  To  find  virtual  images  and  real  images  in 
a  concave  cylindrical  mirror,  and  to  distinguish  between  them. 

Apparatus.  The  cylindrical  mirror  of  the  preceding  experiment 
turned  so  as  to  present  its  concave  side ;  two  matches ;  a  small  pin. 

Directions.  As  shown  in  Fig.  63,  two  radii  should  be 
drawn  from  the  center  of  curvature  to  the  mirror,  and 
between  these  radii  three  arrows  should  be  drawn,  the 
first  1.5cm  from  the  center  of  curvature,  the  second  3.5CI", 
and  the  third  4.2cm. 

Holding  the  mirror  about  25cm  from  the  eye,  look  at 
the  images  of  the  three  arrows. 

Does  each  of  the  three  images  point  from  left  to  right 
as  do  the  arrows  themselves  ? 


REFRACTION. 


211 


Stick  a  -pin  into  the  center  of  one  of  the  arrows,  and  lay 
the  matches,  forming  a  wide  angle  with  each  other,  so 
that  they  shall  point  towards  the  image  of  the  pin.  If  the 
matches,  provided  they  could  be  produced,  are  so  inclined 
to  each  other  as  to  meet  be- 
hind the  mirror,  the  image  is 
virtual;  if  they  are  so  inclined 
to  each  other  as  to  meet  in 
front  of  the  mirror,  the  image 
is  real.  Determine  in  this 
way  the  nature  of  each  of  the 
images,  whether  it  is  real  or 
virtual,  and  record  the  results. 

On  a  sheet  of  paper,  as 
shown  in  Fig.  63,  draw  an 
arrow  about  7cm  distant  from 
the  center  of  curvature. 

Stick  a  pin  into  one  end  of  this  arrow,  and  by  sighting 
as  in  the  last  experiment,  determine  the  position  of  its 
image ;  stick  the  pin  into  the  other  end  of  the  arrow  and 
determine  the  position  of  its  image ;  finally,  stick  the  pin 
into  the  center  of  the  arrow  and  determine  the  position  of 
its  image.  Join  the  three  points  thus  determined,  and 
thus  form  the  image  of  the  arrow. 

Is  this  a  real  or  a  virtual  image  ? 

REFRACTION. 

93.  Refraction  of  Light.  The  object  of  the  next 
experiment  will  be  an  examination  of  the  effect  produced 
upon  the  direction  of  a  ray  of  light  when  the  ray  passes 
from  air  through  a  piece  of  glass  and  into  the  air  again. 


FIG.  63. 


212 


EXPERIMENTAL    PHYSICS. 


Experiment  94.  To  find  the  shape  of  the  path  followed 
by  a  ray  of  light  in  passing  from  an  object  through  a  prism 
to  the  eye. 

Apparatus.  A  prism  with  square  ends ;  a  sheet  of  paper  50cm 
square  ;  four  tacks  ;  four  long  pins. 

Directions.  Lay  the  sheet  of  paper  on  a  table  and 
fasten  it  in  place  by  means  of  the  tacks,  one  at  each  cor- 
ner. On  the  center  of  the  sheet  stand  the  prism  upright 

with  one  of  its  faces  paral- 
lel to  the  right-hand  edge 
of  the  paper,  as  in  Fig.  64. 
Close  to  the  edge  of  the 
paper  farthest  from  you, 
and  a  little  nearer  the 
right-hand  edge  of  the 
paper  than  the  prism, 
stick  one  of  the  pins  up- 
right. Mark  the  position 
of  this  pin  by  the  letter  A. 

Place  the  eye  a  few  centimeters  above  the  edge  of  the 
table  and  look  into  the  prism.  Move  the  eye  to  the  right 
or  left,  if  necessary,  till  the  image  of  the  pin  at  A  is  seen 
through  the  prism.  When  the  image  is  seen,  stick  a  pin 
upright  into  the  paper  near  the  eye,  so  that  this  pin  shall 
just  hide  the  image  when  the  eye  is  kept  stationary. 
Mark  the  position  of  this  pin  by  the  letter  D.  Then  into 
the  paper,  near  the  side  of  the  prism  next  the  eye,  stick 
another  pin  so  that  it  shall  be  in  line  with  the  pin  at  D 
and  with  the  image.  These  two  pins  on  the  side  of  the 
prism  next  the  eye  give  the  direction  in  which  the  ray  of 


FIG.  64. 


REFRACTION.  213 

light  moves  on  emerging  from  the  prism.  To  get  the 
direction  of  the  ray  of  light  that  enters  the  prism  from 
the  pin  at  A,  stick  into  the  paper  on  that  side  a  long 
pin  in  such  a  position  that  its  image  hides,  when  the 
eye  is  in  its  proper  position,  the  image  of  the  pin  at 
A.  With  a  fine-pointed  lead-pencil  draw  a  line  round 
the  end  of  the  prism  on  the  paper.  Remove  the  prism 
and  the  pins.  Lay  a  meter  stick  on  the  paper,  and  draw  a 
line  from  the  position  occupied  by  the  first  pin,  A,  through 
the  position  of  the  pin  next  it  on  the  same  side  of  the 
prism  until  the  line  meets  the  line  representing  the  posi- 
tion of  the  side  of  the  prism.  This  line  represents  the 
incident  ray.  Then  connect  by  a  line  drawn  from  the 
side  of  the  prism  the  positions  of  the  two  other  pins. 
This  line  represents  the  emergent  ray.  As  the  part  of 
the  ray  of  light  in  the  prism  passes  straight  from  the  point 
B  where  the  incident  ray  strikes  the  side  to  the  point  (7, 
whence  the  emergent  ray  leaves  the  prism,  connect  these 
two  points  by  a  straight  line. 

From  an  inspection  of  your  diagram,  how  many  times, 
and  at  what  points,  is  the  ray  of  light  bent  in  passing  from 
the  object  (the  pin  at  A)  through  the  prism  to  the  eye  ? 

From  a  point  outside  the  prism  to  a  point  within  the 
prism  draw,  through  B,  EF  perpendicular  to  the  side  of 
the  prism. 

Definition.  A  ray  of  light  that  falls  upon  a  substance 
is  called  an  incident  ray  (A  B  in  your  diagram) ;  if  the  sub- 
stance is  one  like,  glass  or  water  which  allows  the  ray  to 
enter,  the  ray  after  entering  is  called  the  refracted  ray  (BO 
in  your  diagram). 


214  EXPERIMENTAL   PHYSICS. 

The  perpendicular  to  the  surface  drawn  through  the 
point  of  incidence,  that  is,  the  point  at  which  the  ray 
strikes  the  surface,  is  called  the  normal. 

The  angle  ABE,  between  the  incident  ray  and  that  part 
of  the  normal  lying  in  the  medium  (air  in  this  case)  in 
which  is  the  incident  ray,  is  called  the  angle  of  incidence  ; 
while  the  angle  FBC,  between  the  refracted  ray  and  that 
part  of  the  normal  lying  in  the  medium  (glass  in  this 
case)  in  which  is  the  refracted  ray,  is  called  the  angle  of 
refraction.  >r\  .  v 

By  inspection  of  your  diagram,  which  is  the  smaller, 
the  angle  of  incidence  or  the  angle  of  refraction  ? 

In  the  same  manner  draw  at  the  other  face  of  the  prism, 
whence  the  emergent  ray  leaves,  a  perpendicular,  produc- 
ing it  a  little  way  into  the  prism.  Letter  the  end  of  this 
perpendicular  which  lies  within  the  prism  G-,  and  the  end 
that  lies  without  H. 

Which  is  the  smaller,  the  angle  of  internal  incidence, 
BCGr,  or  the  angle  of  external  refraction,  HOD? 

When  a  ray  of  light  passes  from  a  dense  medium  like 
glass  into  a  rare  one  like  air,  is  the  ray  bent  away  from 
the  normal  or  towards  it  ? 

Show  by  a  sketch  that  a  ray  of  light  falling  obliquely 
upon  a  pane  of  glass  has  the  same  direction  after  emerging 
from  the  glass  as  it  had  before  entering  it. 

Definition.  Refraction  is  the  bending  of  a  ray  of  light 
in  passing  from  one  medium  into  another. 

94.  A  Phenomenon  explained.  When  looking  into 
a  clear  pool  of  water  perhaps  you  have  tried  to  touch 


REFRACTION. 


215 


some  object  at  the  bottom  with  a  stick ;  unless  the  object 
lies  directly  beneath  the  eye,  the  stick  to  strike  the  object 
must  not  be  thrust  straight  towards  the  point  where  the 
object  appears  to  be,  but  behind  it.  An  oar  when  dipped 
into  water  appears  bent.  A  straight  post  standing  in 
water  also  presents  a  very  curious  phenomenon.  To  the 
observer,  shown  on  the  bank  in  Fig.  65,  the  part  of  the 
post  which  is  beneath  the  surface  of  the  water  appears  to 
be  shorter  than  it  really  is.  This  phenomenon  is  due 


to  the  refraction,  on  emerging  into  the  air,  of  the  rays  of 
light  proceeding  from  the  part  of  the  post  under  the 
water.  The  eye  of  the  observer  is  deceived  by  these 
refracted  rays.  It  is  unaware  of  the  bending  of  the  rays 
at  the  surface  of  the  water,  and  so  the  object  appears  in 
the  direction  whence  the  rays  come  on  leaving  the  water. 


216 


EXPERIMENTAL   PHYSICS. 


The  apparent  bending  of  an  oar,  when  dipped  into 
water,  is  explained  in  the  same  manner. 

95.  Index  of  Kefractioii.  We  found,  when  studying 
the  subject  of  the  reflection  of  light,  that  the  angle  of 
reflection  was  equal  to  the  angle  of  incidence  ;  but  on 
coming  to  the  study  of  the  refraction  of  light,  we  found 
that  the  angle  of  refraction  is  not  equal  to  the  angle 
of  incidence,  being  smaller  than  the  angle  of  incidence 

if  the  ray  passes  from  a  rare 
into  a  dense  medium,  but 
larger  if  the  ray  passes 
from  a  dense  into  a  rare 
medium. 

There  is,  however,  a  some- 
what remote  relation  be- 
tween the  angle  of  incidence 
and  the  angle  of  refraction, 
which  can  be  illustrated  by 
the  help  of  Fig.  66.  Let 
AB  represent  the  surface  at 
which  refraction  takes  place  ;  10  and  OR,  the  incident 
ray  and  the  refracted  ray ;  MN,  the  normal  to  AB  at  0, 
the  point  where  the  ray  pierces  the  surface.  With  0  as 
center  and  any  convenient  radius,  describe  a  circumference 
AMBN.  From  I  and  R  respectively  draw  IE  and  RH 
perpendicular  to  MN.  Let  TO  represent  another  inci- 
dent ray,  and  R'  0  another  refracted  ray,  and  I'K  and 
R'  G-  the  perpendiculars. 

Now  physicists  have  found  by  experiment  that  the  ratio 

IE 

nrrt  which  is  called  the  index  of  refraction,  is  always  equal 


REFRACTION. 


217 


to  the  ratio  ^-^,  as  long  as  no  change  is  made  in  the  two 
-K  Cr 

mediums ;  if  one  medium  is  air  and  the  other  glass,  then 
the  index*  of  refraction  has  a  uniform  numerical  value,  no 
matter  at  what  angle  the  incident  ray  enters;  but  if  for 
glass  we  substitute  water,  then  the  index  of  refraction 
assumes  a  new  value. 

Turn  back  to  Exp.  94,  and  in  your  diagram  (which 
should  have  been  very  accurately  constructed;  if  not 
accurately  constructed,  it  must  be  drawn  afresh),  with  the 
point  B  as  a  center,  describe  a  circumference  which  shall 
cut  the  normal  in  two  points,  and  also  cut  the  incident 
ray  and  the  part  of  the  ray  in  the  glass.  Draw  IE 
and  RH,  and  with  a  pair  of  dividers  carefully  measure 
the  length  of  each  of  these  lines. 
Divide  the  greater  length  by  the 
smaller.  Record  the  result. 

Also  with  O  as  a  center  repeat 
the  process.  Record  the  result. 

Experiment  95.  To  find  the  in- 
dex of  refraction  from  air  to  water, 
by  Hall's  method. 

Apparatus.  A  glass  jar;  a  brass 
partition  to  fit  the  jar;  a  brass  index ; 
a  meter  stick  ;  a  sheet  of  paper. 


FIG.  67. 


Directions.  Put  the  partition 
in  place  in  the  jar  (Fig.  67),  and 
also  the  brass  index.  Pour  water  into  the  jar  till  its 
level  comes  within  2mm  of  the  middle  tooth  of  the  par- 
tition. Then,  looking  through  the  side  of  the  jar,  add 
water  cautiously  till  the  level  of  the  water  is  less  than 


218  EXPERIMENTAL    PHYSICS. 

0.5mm'from  the  tooth.  With  the  eye  about  25cm  from  the 
edge  of  the  jar,  sighting  in  a  line  with  the  edge  of  the  jar 
and  the  lower  edge  of  the  tooth,  adjust  the  index  till  its 
tip  seems  to  lie  in  this  line  produced.  After  these  adjust- 
ments have  been  carefully  made,  look  to  see  whether  the 
water  touches  the  tooth.  In  case  the  water  has  wet  the 
lower  edge  of  the  tooth,  all  the  adjustments  must  be  made 
again. 

Then  measure  and  record  the  internal  diameter,  and 
also  the  distance  of  the  lower  edge  of  the  tooth  below  the 
edge  of  the  jar.  Carefully  measure,  on  the  outside  of  the 
jar,  the  distance  of  the  tip  of  the  index  below  the  edge  of 
the  jar. 

Having  completed  the  measurements,  make  carefully 
a  .full-sized  diagram  of  the  sides  of  the  jar,  as  shown  in 
Fig.  68.  Draw  the  partition  6r<7,  mak- 
ing Gr  C  in  length  equal  to  the  distance 
of  the  lower  edge  of  the  tooth  below 
the  edge  of  the  jar.  Produce  GrC  by 
a  dotted  line.  Through  C  draw  a 
horizontal  line  to  represent  the  surface 
of  the  water.  Mark  the  position  of 
_P,  the  tip  of  the  index,  and  draw  PC, 
which  represents  the  direction  of  the 
ray  before  leaving  the  water,  and  draw  CR,  representing  the 
refracted  ray.  With  any  convenient  radius,  as  CR,  and 
with  C  as  a  center,  describe  the  arc  RI,  cutting  CR  in 
R,  and  PC  in  I.  From  R  drop  the  perpendicular  RGr 
on  G-C,  and  from  /drop  the  perpendicular  IE  on  G-C  pro- 
duced. Measure  carefully  IE  and  R  Gr. 


LENSES    AND    PRISMS.  219 

TTJ 

The  ratio  -—  -  is  the  index  of  refraction  from  water  to 


7?  '  C1 

air,  while  the  ratio  is  the  index  of  refraction  from  air 

IJii 

to  water. 

Compute  each  of  these  ratios. 

It  is  a  good  plan  to  put  the  index  on  the  side  of  the  jar 
opposite  the  first  position  of  the  index,  without  disturb- 
ing the  partition,  and  make  a  new  adjustment.  The  aver- 
age of  the  two  results  obtained  from  the  two  sets  of 
measurements  will  give  the  index  of  refraction  with 
greater  accuracy,  as  by  this  means  errors  due  to  the 
unevenness  of  the  edge  of  the  jar  and  to  the  position  of 
the  partition  will  be  made  very  small. 


LENSES    AND    PRISMS. 

96.  Relation  between  Lenses  and  Prisms.  Suppose 
we  have  a  number  of  prisms,  one  of  which  we  place  at  r ; 
then  a  ray  of  light,  Ar,  from  a  spot  of  light,  J.,  after 


FIG.  69. 


passing  through  the  prism,  is  refracted.  If  at  w  a  prism 
exactly  like  that  at  r  is  placed,  as  shown  in  Fig.  69,  it 
will  refract  the  ray,  Aw.  Let  us  denote  by  B  the  point 
of  intersection  of  the  two  refracted  rays.  By  using  some- 


220 


EXPERIMENTAL    PHYSICS. 


what  smaller  prisms  we  can,  by  trial,  find  positions  s  and 
v,  so  that  these  prisms  will  refract  rays  from  A  to  B. 
Similarly  positions  for  another  pair  of  prisms  could  be 
found;  call  these  positions  t  and  u.  Now  a  lens  may 


be  regarded  as  made  up  of  so  great  a 
number  of  prisms  that  the  joinings  be- 
come smooth,  as  shown  in  the  diagrams 
in  Fig.  70. 


FIG.  70. 


97.    Definitions  Relating  to  Lenses. 

Lenses  are  commonly  made  of  glass,  and 
their  surfaces  are  usually  portions  of  the  surfaces  of 
spheres.  In  the  simplest  case  the  bounding  surfaces  are 
of  equal  radii. 

The  centers  of  curvature  of  a  lens  are  the  points  0  and  0', 
that  is,  the  centers  of  the  spheres  (Fig.  71)  whose  inter- 
section forms  the  lens. 

The  principal  axis  of  a  lens  is  a  straight  line  of  indefi- 


FIG.  71. 


FIG.  72. 


nite  length  drawn  through  the  centers  (0,  Or)  of  curva- 
ture.    In  Fig.  71  AB  represents  the  principal  axis. 

The  optical  center  of  a  lens  is  a  point,  C  in  Fig.  72,  so 
situated  that  a  ray,  ABCDE,  passing  through  it  has  the 


LENSES   AND   PRISMS. 


221 


FIG.  73. 


same  direction  after  leaving  the  lens  as  before  entering  it. 
The  position  of  the  optical  center  depends  upon  the  shape 
of  the  lens.  For  a  lens  like  that  represented  by  the 
figure,  where  the  two  sides  are  curved  alike,  the  optical 
center  of  the  lens  is 
at  the  middle  of  the 
lens. 

A  secondary  axis  of 
a  lens  is  any  straight 
line,  except  the  prin- 
cipal axis,  drawn 
through  the  optical  center.  In  Fig.  72  MM  represents 
such  an  axis.  There  are  an  infinite  number  of  such  axes. 

The  principal  focus  of  a  convex  lens  is  the  point  at 
which  the  rays,  parallel  before  entering  the  lens,  cross 
after  passing  through  the  lens. 

In  Fig.  73  the  point  F  is  the  principal  focus.  It  will 
be  noticed  that  the  rays  before  entering  the  lens  are 
parallel,  but  that  the  lens  bends  them  so  that  they  meet 
after  emerging. 

98.  Names  and  Properties  of  Different  Kinds  of 
Lenses.  In  the  following  list  is  given  the  name,  and 

after  it  the  description  of  each 
lens.  The  numbers  refer  to  the 
diagrams  of  Fig.  74. 

1.  Double    convex    lens,    both 
surfaces  convex. 

2.  Plano-convex,    one    surface 
convex,  one  plane. 

3.  Concavo-convex,  converging,  one  surface  convex,  one 
concave. 


FIG.  74. 


222 


EXPERIMENTAL   PHYSICS. 


FIG.  74. 


1,  2,  and  3  are  called  converging  lenses,  because  parallel 
rays  of  light,  after  passing  through  them,  converge.  Notice 
that  they  are  thickest  in  the  middle. 

4.  Double    concave,   both   sur- 
faces concave. 

5.  Plano-concave,    one    surface 
concave,  one  plane. 

6.  Concavo-convex,    diverging, 
one  surface  concave,  one  convex. 

4,  5,  and  6  are  called  diverging 
lenses,  because  parallel  rays  of  light,  after  passing  through 
them,  diverge.    Notice  that  they  are  thinnest  in  the  middle. 
3  and  6  are  also  called  meniscus  lenses. 

REAL    IMAGES. 

99.  Focal  Length;  Conjugate  Foci.  The  object  of 
the  next  two  experiments  will  be  to  make  clear  the  mean- 
ing of  the  terms  focal  length  and  conjugate  foci. 

Experiment  96.  To  find  the  focal  length  of  a  double 
convex  lens. 

Apparatus.  A  spectacle  lens ;  a  meter  stick ;  two  blocks  each 
with  a  groove  to  slide  on  the  meter  stick  ;  a  piece  of  cardboard  10cm 
square ;  colored  glasses. 

Directions.  Stand  the  piece  of  cardboard  in  the  open- 
ing in  the  top  of  one  of  the  blocks,  as  shown  in  Fig.  75, 
and  the  lens  with  its  longest  diameter  vertical  in  the 
opening  in  the  top  of  the  other  block.  It  is  well  to 
cement  the  lens  in  place  by  dipping  the  edge  in  a  mixture 
of  equal  parts  of  melted  beeswax  and  rosin.  On  the 
meter  stick  place  the  screen  and  the  lens  with  its  prin- 


REAL    IMAGES. 


223 


cipal  axis  parallel  to  the  length  of  the  rod.  Point  the 
lens  toward  the  sun,  so  that  the  sun's  rays  shall  pass 
through  the  lens  and  fall  upon  the  screen.  In  order  not 
to  dazzle  the  eyes,  look  at  the  bright  spots  on  the  screen 
through  colored  glasses.  Move  the  lens  back  and  forth 
on  the  rod  until  a  position  is  found  that  gives  on  the 
screen  a  sharp  image  of  the  sun.  The  distance  from  the 
lens  to  the  screen  as  now  arranged  is  called  the  focal 


FIG.  75. 

length  of  the  lens.  Record  in  your  note-book  the  position 
of  the  lens  on  the  meter  stick,  that  is,  the  number  of  cen- 
timeters it  is  from  one  end  of  the  rod,  and  also  record  the 
position  of  the  screen,  that  is,  the  number  of  centimeters 
it  is  from  the  end  of  the  rod  from  which  you  measured 
the  distance  of  the  lens.  You  will  notice  a  mark  carried 
round  each  block  to  the  meter  stick  to  assist  you  in  mak- 
ing these  measurements. 

What  will  the  difference  of  these  two  readings  give  ? 

Make  a  change  in  position  of  the  screen  on  the  meter 
stick,  and  adjust  the  lens  till  you  again  get  a  sharp  image 
of  the  sun  on  the  screen.  Take  the  measurements  and 
record  as  before.  Repeat  three  times  and  record,  mak- 


224  EXPERIMENTAL   PHYSICS. 

ing  five  measurements  of  the  focal  length  in  all.  Find  the 
average  of  the  five  measurements. 

The  rays  of  light  from  the  sun  are  practically  parallel, 
and  on  passing  through  the  lens  are  bent  so  as  to  pass 
through  the  principal  focus. 

Suppose  a  luminous  point  placed  at  the  principal  focus, 
what  effect  would  the  lens  have  on  the  rays  diverging 
from  the  point? 

Experiment  97.  To  find  the  relation  between  conjugate 
focal  distances  of  a  lens  and  its  focal  length. 

Apparatus.  The  same  as  in  Exp.  96,  and  in  addition  a  small 
kerosene  lamp.  Use  the  same  lens  as  in  Exp.  96. 

Directions.  Over  a  smoky  flame  hold  the  lamp  chim- 
ney till  its  outer  surface  is  covered  with  soot.  Light  the 
wick  of  the  lamp.  Put  the  chimney  in  place,  and  with  a 
sharp-pointed  pin  draw  an  upright  arrow,  as  shown  in 
Fig.  76,  in  the  soot  on  the  chimney  opposite  the  bright 
part  of  the  flame.  Have  the  lines  of  the  arrow  very  fine. 
Perform  this  experiment  in  a  darkened  room. 

Place  one  end  of  the  meter  stick  as  nearly  as  possible 
directly  beneath  this  arrow,  and  at  the  opposite  extremity 
of  this  stick  put  the  cardboard  screen,  so  that  its  center 
shall  be  over  the  end  of  the  stick.  Support  this  end  of  the 
meter  stick  on  a  block.  Set  the  lens  on  the  stick  near 
the  lamp,  and  then  slide  it  away  from  the  lamp  till  a  dis- 
tinct image  of  the  arrow  (which  we  call  the  object)  appears 
on  the  screen.  Read  in  centimeters  the  distance  from  the 
center  of  the  lens  to  the  arrow  on  the  chimney,  and 
record  this  distance  in  a  column  headed  D0.  (D  stands  for 
distance,  and  the  letter  o  placed  to  the  right  and  a  little 


REAL   IMAGES.  225 

below  stands  for  object :  so  D0  is  an  abbreviation  for  "  the 
distance  from  the  lens  to  the  object.")  Measure  in  centi- 
meters, and  record,  in  a  column  headed  D^  the  distance 
from  the  center  of  the  lens  to  the  image  on  the  screen. 
(Di  stands  for  "  the  distance  from  the  lens  to  the  image.") 
Without  moving  anything  but  the  lens,  slide  that  along 
the  stick  till  it  again  throws  upon  the  screen  a  distinct 
image  of  the  arrow.  Record  the  distance  of  the  lens  from 
the  lamp  in  the  column  headed  D0,  and  the  distance  of 


FIG.  76. 


the  lens  from  the  screen  in  the  column  headed  D{.  Then 
place  the  screen  at  a  distance  of  80cm  from  the  arrow  on 
the  chimney,  and  proceed  as  before. 

Place  the  screen  at  distances  of  70cm,  65cm,  60cm, 
from  the  arrow  on  the  chimney,  making  records  in  the 
columns  headed  D0  and  D{,  till  the  lens  ceases  to  throw  a 
distinct  image  of  the  arrow  upon  the  screen.  In  all,  the 
screen  should  be  put  in  five  or  six  different  positions.  If, 
with  the  lens  which  you  have,  you  are  unable  to  get  dis- 
tinct images  for  five  or  six  different  positions  of  the  screen, 
start  with  the  screen  at  a  distance  of  more  than  100cm 
from  the  arrow  on  the  chimney,  and  then  move  the  screen 
towards  the  arrow  about  10cm  at  a  time. 

Let  F  denote  the  focal  length  of  the  lens  as  already 

found.     Express  in  every  case  the  quantities  —  and  — •  as 

•U f\  -Lr* 


226  EXPERIMENTAL   PHYSICS. 

decimals,  then  add  them  (that  is,  add  —  and  —  expressed 

JJ0  .L/i 

as  decimals),  and  see  how  the  sum  in  each  case  compares 
with  —  expressed  as  a  decimal. 

Definition.  Conjugate  foci  of  a  lens  are  any  two  points 
so  situated  with  respect  to  the  lens  that  an  object  at  either  of 
them  will  produce  an  image  at  the  other. 

How  many  conjugate  foci  can  your  lens  have  ? 

Look  over  the  results  of  the  experiment  just  performed, 
and  answer  the  following  questions  : 

If  the  distance  between  the  lens  and  the  object  (the 
arrow)  is  increased,  does  the  distance  between  the  image 
and  the  lens  increase  or  decrease  ? 

When  the  distance  from  the  lens  to  the  object  is  large, 
is  the  image  large  or  small  ? 

When  the  lens  is  a  long  distance  from  the  object,  is  the 
image  near  the  principal  focus  ? 

1OO.  Parallax.  If  the  distance  of  the  object  from  an 
ordinary  lens  is  several  hundred  meters,  the  image  practi- 
cally coincides  with  the  principal  focus.  A  second  way  is 
thus  suggested  of  finding  the  principal  focus  of  a  lens,  and, 
consequently,  the  focal  length.  You  have  already  found  the 
principal  focus  of  a  lens  in  Exp.  96.  If  you  look  through 
a  lens  at  a  distant  object  such  as  a  chimney,  you  will  see 
an  inverted  image  of  the  chimney.  If  you  can  locate  the 
position  of  the  image  (a  screen  cannot  be  used  for  the 
purpose  in  this  case),  the  distance  from  the  lens  to  the 
image  will  be  the  focal  length  of  the  lens.  A  peculiar 


KEAL   IMAGES.  227 

means  is  employed  to  find  the  position  of  the  image,  which 
depends  on  the  following  facts : 

When  traveling  by  rail  and  looking  from  the  window 
at  the  distant  landscape,  you  have  doubtless  observed  that 
objects  at  different  distances  are  left  behind  at  different 
rates,  those  not  far  from  the  train  rapidly,  those  at  a  great 
distance  slowly;  consequently,  they  seem  to  move  past  one 
another.  This  apparent  relative  shift  of  objects  due  to  a 
change  in  the  observer's  position  is  called  parallax. 

To  illustrate  the  meaning  of  parallax  still  further,  hold 
your  two  forefingers  upright  in  line  with  each  other  and 
with  the  eye.  Fix  the  eye  on  the  nearer  finger  and  slowly 
move  the  head  from  side  to  side  by  slightly  bending  the 
neck.  The  finger  that  is  farther  from  the  eye  will  appear 
to  move  in  the  same  direction  as  the  head.  Now  bring 
the  more  distant  finger  nearer  the  other,  the  relative 
motion  between  them  becomes  less,  and  finally,  when  the 
fingers  are  close  together,  there  is  no  relative  motion.  It 
will  be  well  to  keep  in  mind  the  following : 

Rule.  When  two  objects  are  in  the  same  general  direction 
but  unequally  distant  from  an  observer,  the  more  distant 
object  appears  to  move,  with  respect  to  the  nearer,  in  the  same 
direction  as  that  in  which  the  observer's  eye  is  moving. 

Experiment  98.  To  find,  by  the  method  of  parallax,  the 
focal  length  of  a  double  convex  lens. 

Apparatus.  The  lens  already  used,  mounted  on  a  meter  stick ; 
a  block  to  slide  on  the  meter  stick  with  a  long  pin  stuck  in  a  vertical 
position  into  the  middle  point  of  its  upper  surface. 

Directions.  Open  a  window  from  which  you  can  look 
a  long  distance.  Lay  the  meter  stick  on  the  window  sill. 


228 


EXPERIMENTAL    PHYSICS. 


Put  the  block  carrying  the  pin  in  such  a  position  on  the 
stick  that  it  shall  be  about  as  far  from  the  end  of  the  stick 
as  you  are  accustomed  to  hold  the  printed  page  of  a  book 
from  the  eye  when  reading.  Put  the  lens  on  the  meter 
stick  (Fig.  77),  but  not  between  the  pin  and  the  eye.  Point 
the  stick  toward  some  object,  as  a  chimney  several  hundred 
feet  away.  When  you  look  through  the  lens,  you  will 
see  a  little  image  of  the  chimney,  but  inverted.  This 


FIG.  77. 


image  is  a  real  one,  and  exists  somewhere  in  the  space 
between  the  lens  and  your  eye.  It  must  be  your  purpose 
now  to  determine  accurately  the  distance  from  the  lens  to 
this  image.  Move  the  head  from  side  to  side,  all  the  while 
looking  at  the  image.  According  to  our  rule  (see  page 
227),  if  the  image  is  farther  from  the  eye  than  the  pin  is,  it 
will  move  with  respect  to  the  pin  in  the  same  direction  as 
you  move  your  head ;  consequently,  in  order  to  get  the  image 
of  the  chimney  to  have  the  same  position  as  the  pin,  the 
lens  must  be  moved  towards  the  pin.  On  the  other  hand, 
if,  when  the  head  is  moved  from  side  to  side,  the  image 
moves  with  respect  to  the  pin  in  the  opposite  direction  to 


REAL    IMAGES.  229 

that  in  which  you  move  your  head,  the  image  is  nearer 
the  eye  than  the  pin,  and  to  make  the  image  coincide 
with  the  pin,  the  lens  must  be  pushed  farther  away  from 
the  pin.  Adjust  the  lens  till  there  is  no  relative  motion 
between  the  image  and  the  pin,  that  is,  till  the  two,  on 
moving  the  head,  always  keep  accurately  together. 

Record  the  position  of  the  lens  and  that  of  the  pin. 

What  is  the  focal  length  of  the  lens  in  centimeters  ? 

Repeat  the  setting  and  measurements  several  times. 
As  before,  record  these  measurements. 

How  does  the  average  of  the  results  obtained  by  this 
method  compare  with  that  obtained  in  Exp.  96  ? 

Experiment  99.  To  find  the  position  of  the  real  image 
of  a  near  object,  formed  by  a  double  convex  lens. 

Apparatus.  A  meter  stick ;  a  double  convex  lens ;  three  blocks 
with  grooves  to  slide  on  the  meter  stick ;  two  short  pins. 

Directions.  Put  the  blocks  that  carry  the  pins  on  the 
meter  stick,  with  the  block  carrying  the  lens  between 
them,  as  shown  in  Fig.  78.  Put  one  pin  at  a  distance, 


FIG.  78. 


say,  1.5  times  the  focal  length  away  from  the  lens.  Slide 
the  other  pin  along  the  meter  stick,  using  another  meter 
stick,  if  necessary,  placed  with  its  end  against  that  of  the 
first.  By  the  method  of  parallax,  find  the  position  of  the 
real  image  of  the  first-mentioned  pin.  Changing  nothing, 


230  EXPERIMENTAL   PHYSICS. 

sight  from  the  neighborhood  of  the  first-mentioned  pin 
towards  the  image  of  the  other. 

Does  this  image  coincide  with  the  position  of  the  first- 
mentioned  pin  ? 

Measure  the  distance  from  the  lens  to  each  of  the  pins. 

Make  another  setting ;  measure  and  record  the  distances. 

From  the  measurements  compute  the  focal  length  of 
the  lens. 

Explain  how  this  experiment  has  illustrated  the  mean- 
ing of  the  term  conjugate  foci. 

Experiment  1OO.  To  find  the  shape  and  the  size  of  a 
real  image,  formed  by  a  converging  lens  (double  convex),  as 
compared  with  the' shape  and  the  size  of  the  object. 

Apparatus.  The  lens  mounted  on  a  block;  a  sheet  of  blank 
paper  100cm  long  and  50cm  wide  ;  a  meter  stick :  two  pins,  one  long, 
the  other  short. 

Directions.  Spread  the  paper  smoothly  on  a  table,  and 
fasten  it  at  the  corners  by  means  of  tacks.  Have  the 
sheet  laid  with  one  end  near  the  edge  of  the  table.  Draw 
a  line  from  the  middle  of  one  end  of  the  sheet  to  the 
middle  of  the  other  end.  At  a  distance  of  2cm  or  3cm  from 
that  end  of  the  sheet  remote  from  the  edge  of  the  table, 
draw  a  line  at  right  angles  to  the  line  first  drawn.  The 
line  last  drawn  should  be  8cm  long,  and  should  extend  4cm 
on  either  side  of  the  line  first  drawn.  Mark  one  end  of 
this  8cm  line  like  the  tip  (Fig.  79)  of  an  arrow.  Divide 
the  arrow  thus  formed  into  four  parts  of  equal  length  by 
means  of  dots. 

Lay  the  block  carrying  the  lens  on  its  side.  Have  the 
edge  of  the  lens  rest  upon  the  paper,  and  the  lens  so 
placed  that  its  axis  is  parallel  to  the  median  line  (the  line 


REAL    IMAGES. 


231 


c 


first  drawn  on  the  paper).     The  center  of  the  lens  must 

be  directly  over  the  median  line  at  a  distance  from  the 

middle  of  the  arrow  about  1.5  times  the  focal  length  of 

the  lens.     If  the  lens  should  be  placed  at  a  distance  less 

than  its  focal  length  from  the  line,  a  virtual  image  would 

be  obtained.     In  order  to  get  the  center  of  the  lens  exactly 

over  the  median  line,  stick  the 

short  pin  upright  into  the  point 

3,  at  the  middle  of  the  arrow. 

Then  stick  the  long  pin  upright 

into  the  median  line  near  the 

edge  of  the  table.     After  you 

have  done  this,  slide  the  lens  a 

little  way  to  the  right  or  to  the 

left  across  the  median  line,  till 

the  image  of  the  small  pin  is 

hidden  by  the  long  pin,  when 

the  eye  is  held  near  the  edge 

of  the  table  and  in  line  with  the 

two  pins.     The   center  of  the 

lens  is  now  over  the  median  line.     The  lens  must  not  be 

moved  during  the  subsequent  parts  of  the  experiment. 

To  locate  the  position  of  the  image  of  3,  move  the  long 
pin  back  and  forth  till,  by  the  method  of  parallax,  you 
make  this  pin  coincide  with  the  image  of  the  short  pin. 
Mark  this  position  I3.  (I  stands  for  "  image,"  and  the 
small  number  placed  to  one  side  and  a  little  below  this 
letter  indicates  the  point  of  the  arrow  into  which  the  pin 
is  stuck.)  Now  stick  the  short  pin  upright  into  the  arrow 
at  the  tip,  which  we  shall  call  point  1,  and  then  on  the 
other  side  of  the  lens  stick  the  long  pin  upright  through 


FIG.  79. 


232  EXPERIMENTAL   PHYSICS. 

the  paper  into  the  table  in  such  a  position  (found  by  the 
method  of  parallax)  as  to  make  it  coincide  with  the  image 
of  the  pin  in  the  tip  of  the  arrow.  Mark  the  position  of 
the  image,  that  is,  the  point  where  the  second  pin  pierces 
the  paper,  Iv  In  the  same  way  locate  the  points  Zj,  /4, 
etc.,  corresponding  to  the  points  2,  4,  etc.,  of  the  arrow. 
The  student  is  warned  in  this  experiment  not  to  let 
any  idea  he  may  have,  as  to  where  an  image-point 
ought  to  be,  interfere  with  his  judgment  as  to  where  the 
point  really  is.  The  five  points,  Iv  Iv  1%,  74,  I5,  outline 
the  image  of  the  arrow  as  the  lens  would  form  it  if  the 
lens  were  lowered  until  its  center  was  on  a  level  with 
the  paper.  Remove  the  lens,  and  mark  by  a  dot  the  point 
on  the  paper  above  which  the  center  of  the  lens  was. 
Then  carefully  draw,  with  a  sharp  lead  pencil,  straight 
lines  joining  each  of  the  object-points  (1,  2,  etc.)  of  the 
arrow  with  its  corresponding  image-point  (Iv  Iv  etc.). 
Measure  the  distance  from  each  object-point  to  the  lens 
(that  is,  to  the  dot  marking  the  position  of  the  center  of 
the  lens).  Measure  the  distance  from  each  of  the  image- 
points  to  the  lens.  Record  all  of  these  measurements. 

Measure  and  record  the  length  of  the  object  and  that  of 
the  image.  If  the  image  is  not  a  straight  line,  measure 
the  distance  from  I±  straight  to  1^  and  also  the  actual 
length  of  the  image,  whatever  its  shape. 

Measure  the  distance  from  point  3  on  the  object  to  the 
lens,  and  from  the  lens  to  the  middle  point  of  the  straight 
line  JjZj.  Record  the  distances. 

Call  the  distance  from  point  3  on  the  object  to  the  lens, 
D0.  Call  the  distance  from  the  middle  point  of  the 
straight  line  I^Ib  to  the  lens,  D^ 


REAL   IMAGES.  233 

Call  the  length  of  the  object,  0. 

Call  the  length  of  the  line  J^,  I. 

Making  use  of  your  measurements,  should  you  say  that 
D0  is  the  same  part  of  D;  as  0  is  of  I? 

Repeat  your  process  of  reasoning,  using  the  distance 
from  object-point  1  to  lens,  and  from  the  lens  to  Iv 
together  with  the  values  of  0  and  /  already  used. 

Can  you,  as  a  result  of  this  examination,  state  any  law 
for  the  relation  between  the  several  distances  and  the 
dimensions  of  the  object  and  of  the  image  ? 

Can  you  explain  the  form  of  the  image  ? 

SUGGESTIONS.  The  middle  of  the  object  is  nearer  the  middle  of  the 
lens  than  the  ends  of  the  object  are.  The  focal  length  of  a  lens,  for  rays 
parallel  to  a  secondary  axis,  is  practically  equal  to  the  focal  length  for 
rays  parallel  to  the  principal  axis.  Consequently,  a  consideration  of  the 

change  made  in  Di  by  a  change  in  D0,  in  the  equation  -  -  +  —  =  — ,  will 

Jj0      Ui      Jb 

be  useful  in  explaining  the  form  of  the  image. 

1O1.  Diagram  to  illustrate  the  Formation  of  a  Real 
Image.  The  images  formed  by  lenses  thus  far  consid- 
ered have  been  real  images,  that  is,  images  that  can  be 
caught  upon  a  screen.  An  inspection  of  the  diagram 
(Fig.  80)  will  show  that  real  images  are  formed  by  the 
actual  crossing  of  the  rays  of  light. 

To  construct  the  real  image  of  an  object : 

Let  AB  denote  the  object,  F  the  principal  focus  of  the 
lens,  0  the  optical  center  of  the  lens,  and  A'B'  the  image. 

From  the  point  A  rays  of  light  are  darting  out  in  all 
directions ;  one  of  these  rays  must,  then,  be  parallel  to  the 
principal  axis.  This  ray,  lettered  AD,  after  going  through 
the  lens  will  pass  through  the  principal  focus,  F.  (Why  ?) 
Another  ray,  A  0,  will  pass  through  the  optical  center,  0 


234 


EXPERIMENTAL    PHYSICS. 


(see  the  Def.  on  page  220),  and  intersect  the  ray  from 
-4,  passing  through  F,  at  A',  forming  a  real  image  of  the 
point  A.  In  like  manner  a  real  image  of  the  point  B  is 
formed  at  B'.  Rays  of  light  going  from  other  points  of 
AB  will  form,  after  passing  through  the  lens,  images  of  the 


FIG.  so. 

points  whence  they  start  out,  so  we  will  connect  the  points 
A*  and  B',  assuming  according  to  the  custom  of  the  books 
on  physics,  that  the  images  of  all  the  points  of  AB  will 
lie  on  the  straight  line  A'B'.  A  B'  is  called  the  image  of 
AB.  If  the  thickness  of  the  lens  is  small  as  compared 
with  the  focal  length  of  the  lens,  there  is  no  great  error 
in  the  assumption  that  A'B'  is  the  image  of  AB.  (Why?) 


EXAMPLES. 

1.  The  focal  length  of  a  double  convex  lens  is  10cm.     An  object  is 
placed  at  a  distance  of  30cm  from  the  lens ;  at  what  distance  from  the 
lens  will  the  image  be  formed  ? 

SUGGESTION.     Make  use  of  the  relation  —  4-  —  =  •=• 

JJ0        JJi       r 

2.  The  focal  length  of  a  double  convex  lens  is  20cm.     The  image  of  an 
object  is  formed  at  a  distance  of  100cm  from  the  lens;  how  far  is  the 
object  from  the  lens  ? 

3.  The  image  of  an  object  placed  at  a  distance  of  100cm  from  a  double 
convex  lens  is  formed  at  a  distance  of  400cm  from  the  lens.     Find  the 
focal  length  of  the  lens. 


VIRTUAL   IMAGES.  235 

4.  Show  by  means  of  the  formula  —  +  —  =  —  what  must  be  the 

D0      Di      t 

distance,  in  terms  of  the  focal  length,  F,  of  object  and  image  from  the 
lens  in  order  that  they  may  be  of  the  same  size. 

5.  At  what  distance  from  a  lens  of  36cm  focal  length  must  an  object 
be  placed  in  order  that  the  dimensions  of  the  inverted  image  shall  be : 

(a)  Half  as  large  as  those  of  the  object  ? 
(6)  Twice  as  large  as  those  of  the  object  ? 


VIRTUAL    IMAGES. 

1O2.  Formation  of  Virtual  Images.  The  object  of 
the  two  following  experiments  is  to  show  the  way  of  form- 
ing virtual  images  by  means  of  a  double  convex  lens. 

Experiment  1O1.  To  find  the  relation  between  the  focal 
length  of  a  lens  and  the  distance  of  the  object  and  the  dis- 
tance of  its  virtual  image. 

Apparatus.  A  meter  stick  ;  a  lens  ;  three  blocks  with  grooves  to 
slide  on  the  meter  stick ;  a  long  pin ;  a  short  pin. 

Directions.  Mount  the  lens  on  one  of  the  blocks,  and 
put  the  block  on  the  meter  stick  at  a  distance  of  about 
3cm  from  one  end.  Lay  the  meter  stick  with  its  narrow 


FIG.  81. 

E,  position  of  eye ;  L,  position  of  lens  ;  S,  position  of  short  pin  ;  T,  position 
of  long  pin. 

edge  on  the  table  and  with  the  end  carrying  the  lens  next 
to  you.  Into  the  center  of  the  top  of  another  block  stick 
the  short  pin.  Place  this  block,  as  shown  in  Fig.  81,  on 


236  EXPERIMENTAL    PHYSICS. 

the  meter  stick  so  that  the  pin  shall  be  between  the  lens 
and  its  principal  focus.  The  pin  must,  however,  be  on 
the  side  of  the  lens  remote  from  the  eye. 

The  long  pin,  stuck  upright  into  the  top  of  the  third 
block,  is  placed  on  the  meter  stick  beyond  the  short  pin. 
As  you  look  through  the  lens  you  will  see  a  virtual  image 
of  the  short  pin.  By  moving  the  long  pin  towards  you 
or  by  pushing  it  further  away,  try  to  locate  the  position  of 
the  image  of  the  short  pin  by  the  method  of  parallax 
already  explained.  The  eye  should  be  held  in  a  position 
which  will  not  allow  a  view  of  any  part  of  the  short  pin 
over  the  top  of  the  lens.  The  long  pin  is  to  be  looked 
at  over  the  lens,  not  through  it.  When  the  long  pin, 
seen  over  the  lens,  and  the  image  of  the  short  pin  keep 
together  as  the  head  is  moved  from  side  to  side,  measure 
and  record  the  distance  from  the  lens  to  the  short  pin,  and 
also  the  distance  from  the  lens  to  the  long  pin  (the  position 
of  the  virtual  image).  Then  make  a  new  setting  of  the 
short  pin,  and  by  adjusting  the  position  of  the  long  pin, 
again  find  the  position  of  the  image.  As  before,  record 
the  readings. 

In    Exp.   97   you    found,   by   substituting    the    proper 

quantities,  that  -—-{--—  =  —,  that  is,  the  reciprocals  of 

D0         JJi         1 

the  object-distance  and  image-distance  added  produce  the 
reciprocal  of  the  focal  distance. 

In  the  present  experiment  the  object-distance  has  always 
been  less  than  the  focal  distance,  but  the  image-distance 
always  greater  than  the  focal  distance. 

Take  the  difference  between  the  reciprocal  of  the  object- 
distance  and  the  reciprocal  of  the  image-distance,  that  is, 


VIRTUAL    IMAGES. 


237 


— ,  and  see  how  this  difference  compares  with  the 

reciprocal,  — ,  of  the  focal  distance. 
Jb 

The  difficulty  often  met  with  in  getting  the  position  of 
the  virtual  image  in  the  experiment  just  performed  intro-. 
duces  an  uncertainty  into  the  value  of  the  focal  length 
calculated  from  the  data  obtained. 

Experiment  1O2.  To  find  the  shape  and  the  size  of  a  vir- 
tual image,  formed  by  a  converging  lens  (double  convex),  as 
compared  with  the  shape  and  the  size  of  the  object. 

Apparatus.  The  same  as  that  used  in  Exp.  100  with  a  fresh  sheet 
of  paper. 

Directions.  Fasten  the  paper  on  the  table  in  the  same 
position  as  for  Exp.  100.  Draw  a  median  line  lengthwise 
of  the  paper.  Place  the  lens  on 
its  side,  as  in  Exp.  100,  but  at 
a  distance  of  about  20cm  from 
the  end  of  the  paper  nearest 
the  edge  of  the  table.  On  the 
median  line,  on  the  side  of  the 
lens  remote  from  the  edge  of 
the  table,  make  a  dot  at  a  dis- 
tance from  the  lens  equal  to 
about  two-thirds  its  focal  length. 
Through  this  dot  draw  a  line  at 
right  angles  to  the  median  line. 
This  line  should  be  5cm  long  and 
should  be  bisected  by  the  median 

line.     Mark  one  end  of  this  line  like  the  tip  of  an  arrow. 
Divide  the  arrow  into  five  equal  parts,  as  indicated  in  Fig.  82. 


238  EXPERIMENTAL   PHYSICS. 

In  order  to  get  the  center  of  the  lens  over  the  median 
line,  stick  the  short  pin  upright  into  the  middle  of  the 
arrow,  at  the  point  where  it  crosses  the  median  line. 
Stick  the  long  pin  upright  into  the  median  line,  at  the 
end  of  the  paper  remote  from  the  lens.  Look  through 
the  lens  with  the  eye  in  line  with  the  two  pins,  and  slide 
the  lens  a  little  way  to  the  right  or  to  the  left,  across  the 
median  line,  till  the  image  of  the  short  pin  is  in  line  with 
the  two  pins.  When  the  image  is  in  line  with  the  two 
pins,  the  center  of  the  lens  is  over  the  median  line. 

Stick  the  short  pin  upright  through  point  1.  Look 
through  the  lens  and  locate,  by  means  of  the  long  pin,  the 
position  of  the  image  of  the  short  pin.  As  this  image  is 
virtual,  it  will  appear  on  the  same  side  of  the  lens  as  is 
the  object. 

In  this  manner  locate  the  position  of  the  image  of  the 
short  pin  for  each  of  the  remaining  five  points.  Draw 
lines  and  make  measurements  similar  to  those  of  Exp.  100. 

Is  there  any  distinction  between  the  form  of  the  image 
obtained  in  this  experiment  and  the  form  of  the  image  ob- 
tained in  Exp.  100  ? 

What  relations  can  you  make  out,  from  your  measure- 
ments, between  the  distance  of  object  and  image  from  the 
lens  and  their  lengths  ? 

1O3.  Diagram  to  illustrate  the  Formation  of  a  Vir- 
tual Image.  By  an  inspection  of  the  diagram  (Fig.  83) 
it  will  be  seen  that  a  virtual  image  is  formed  not  by  the 
actual  crossing  of  the  rays  of  light,  but  by  their  apparent 
crossing. 

To  construct  the  virtual  image  of  an  object: 


VIRTUAL    IMAGES.  239 

Let  AB  denote  the  object,  F  the  principal  focus  of  the 
lens,  0  the  optical  center  of  the  lens,  and'^L'.B'  the  image 
which  we  wish  to  find.  From  A  rays  of  light  are  darting 
out  in  all  directions;  one  of  these  rays  must,  then,  be 
parallel  to  the  principal  axis.  This  ray,  lettered  AD, 
after  going  through  the  lens  will  pass  through  the  princi- 
pal focus,  F.  (Why?)  Another  ray,  A  C,  will  pass  through 
the  optical  center,  0.  (See  the  Def.  on  page  220.)  The 
bending  of  the  ray,  ADKF,  deceives  the  eye,  and  the  point 


FIG.  83. 

A  appears  to  lie  on  the  prolongation  of  FK-,  the  point  A 
also  lies  on  the  line  J(7,  hence  the  point  A  appears  to  lie 
at  the  intersection  of  FK  produced  and  1C  produced,  or 
at  A'.  A'  is  the  virtual  image  of  A.  The  point  A'  is 
not  the  point  from  which  the  rays  of  light  actually  come, 
but  it  is  the  point  from  which  to  the  eye  they  appear  to 
come. 

By  a  similar  process  B'  is  found  to  be  the  virtual  image 
oiB. 

The  image,  A'B',  is  larger  than  the  object,  AB.  When- 
ever an  object  is  placed  between  a  convex  lens  and  its 
principal  focus,  a  virtual  image  is  seen  on  looking  in  from 
the  other  side  of  the  lens.  As  the  image  is  always  mag- 


240  EXPERIMENTAL    PHYSICS. 

nified,  or  enlarged,  the  name  magnifying  glass  is  commonly 
given  to  a  lens  used  in  this  way. 

In  order  that  the  straight  line  A'B'  may  represent  the 
image,  with  very  small  error,  must  the  thickness  of  the  lens 
be  large  or  small  as  compared  with  the  focal  length  of 
the  lens? 

104.  Velocity  of  Light.     There  are  four  moons  which 
revolve  about  the  planet  Jupiter.     At  times  a  moon  will 
be  visible,  at  others  eclipsed.     The  exact  time  can  be  cal- 
culated at  which  an  eclipse  can  be  seen  from  the  earth, 
when  the  earth  is  in  that  part  of  its  orbit  nearest  Jupiter; 
but  as  the  earth  recedes  from  Jupiter,  the  eclipses  do 
not   occur  on   time,  but  occur   later  and   later  till   the 
earth  reaches  that  part  of   its  orbit  most  distant  from 
Jupiter,  when  the  eclipses  are  16  minutes  and  36  seconds 
behind  time.     As  the  earth  sweeps  round  in  its  orbit  and 
approaches    Jupiter,  the    eclipses  occur  more   and   more 
nearly  on  time,  and  when  the  earth  and  Jupiter  are  near- 
est each  other,  the  eclipses  are   once  more  precisely  on 
time.     This  discrepancy  between  the  computed  time  at 
which  the  eclipse  should  take  place  and  the  actual  time 
at  which  the  eclipse  is  seen,  when  the  earth  is  most  remote 
from  Jupiter,  is  due  to  the  fact  that  the  light  has  taken 
16  minutes  and  36  seconds  in  crossing  the  earth's  orbit, 
a  distance  of  about  190,000,000   miles.     This  gives,  by 
dividing  190,000,000  by  996  (the  number  of  seconds  in 
16  minutes  and  36  seconds),  the  velocity  of  light  to  be 
about  190,000  miles  per  second. 

105.  Nature  of  Light.     All  men  of  science  are  agreed 
that  a  ray  of  light  represents   a  motion  of  some  kind. 


VIRTUAL   IMAGES.  241 

Whenever  a  stone  is  thrown  from  the  hand,  or  an  arrow 
shot  from  a  bow,  we  know  that  either  of  them  will  be  pro- 
pelled through  the  air  with  a  velocity  which  depends  upon 
the  weight  and  the  shape  of  the  object,  and  also  upon  the 
force  employed  in  its  discharge.  When  we  hear  that  light 
has  a  velocity  of  about  190,000  miles  per  second,  we  feel  a 
keen  interest  to  know  what  is  the  nature  of  the  motion 
that  is  propagated  through  a  distance  so  great  in  so  short 
a  period  of  time. 

Two  hypotheses  have  been  advanced  for  explaining  the 
nature  of  light,  the  corpuscular  hypothesis  and  the  wave 
hypothesis. 

The  corpuscular  hypothesis,  long  supported  by  the  author- 
ity of  Sir  Isaac  Newton,  supposes,  in  brief,  that  particles, 
called  corpuscles,  so  very  minute  that  they  cannot  be 
weighed  are  given  out  bodily,  like  sparks,  from  the  sun, 
the  fixed  stars,  and  all  luminous  bodies.  It  is  further 
supposed  that  these  particles  travel  with  enormous  veloc- 
ity, and  excite  the  sensation  of  vision  by  striking  against 
the  eye. 

As  this  hypothesis  failed  to  explain  all  the  facts  known 
about  light,  the  hypothesis  was  abandoned  early  in  the 
nineteenth  century  in  favor  of  the  wave  hypothesis,  which 
has  not  only  explained  all  the  facts  about  light  with 
which  we  are  acquainted,  but  has  also  made  predictions 
about  light  which  have  subsequently  been  verified  by 
experiment.  The  wave  hypothesis  supposes  the  existence 
of  a  substance,  called  the  ether,  which  occupies  all  space, 
not  only  the  regions  between  the  stars,  but  also  the  spaces 
between  the  molecules  of  all  bodies.  This  hypothesis  also 
supposes  that  a  luminous  body  has  the  power  to  cause 


242  EXPERIMENTAL   PHYSIOS. 

waves  in  the  ether,  which  travel  with  great  rapidity,  and  on 
striking  the  eye  produce  the  sensation  which  we  call  light. 

When  we  studied  the  subject  of  wave-motion,  we  found 
that  it  was  possible  for  two  water  waves  of  equal  size  to 
interfere  in  such  a  way  as  to  produce  a  calm.  In  the  sub- 
ject of  sound  we  found  that  two  equal  sound  waves  could 
interfere  to  produce  silence.  In  light,  two  light  waves 
can  interfere  and  produce  darkness,  as  can  be  readily  seen 
by  looking  at  a  flame  through  a  narrow  slit  cut  by  a  pen- 
knife in  a  card.  Very  narrow  black  bands  will  be  seen 
running  parallel  to  the  slit  on  each  side  of  it.  These 
black  bands  are  formed  by  the  interference  of  the  light 
which  is  reflected  from  the  edges  of  the  slit.  These  edges 
correspond  to  the  two  centers  of  disturbance  that  we  con- 
sidered when  examining  the  interference  of  two  sets  of 
water  waves. 

As  an  example  of  one  of  the  remarkable  predictions  of 
the  wave  hypothesis  of  light,  perhaps  the  following  will 
serve  as  well  as  any.  By  a  mere  manipulation  of  the 
mathematical  symbols  by  which  the  wave  hypothesis  is 
expressed,  it  was  shown  that  by  stopping,  in  a  certain 
way,  a  portion  of  the  rays  of  light  passing  through  a 
circular  opening,  the  illumination  of  a  point  upon  a  screen 
behind  the  opening  would  be  greatly  increased.  On  per- 
forming the  experiment  which  the  mathematical  formulae 
suggested,  the  prediction  about  the  increase  of  illumina- 
tion was  verified. 

We  must  bear  in  mind,  however,  that,  although  the 
hypothesis  of  the  existence  of  the  ether  has  enabled  us  to 
explain  the  known  facts  about  light,  it  does  not  by  any 
means  follow  that  the  ether  has  an  actual  existence,  not 


VIRTUAL    IMAGES.  243 

even  if  facts  have  been  predicted  by  its'  aid.  For  when- 
ever a  mass  of  facts,  like  those  connected  with  the  phe- 
nomena of  light,  is  collected,  and  a  means  found  to  bind 
the  facts  together  and  to  explain  them,  it  cannot  be  at  all 
surprising,  if  certain  facts,  of  which  we  were  ignorant, 
should  be  included  in  the  collection.  These  facts  of 
which  we  were  ignorant  will  be  found  when  we  carefully 
examine  the  collection. 


EXAMPLES. 

1.  In  determining  the  illuminating  power  of  a  gas  flame  by  Bunsen's 
photometer,  the  distance  from  the  gas  flame  to  the  grease  spot  was  90cm, 
and  from  the  grease  spot  to  the  standard  candle  35cm.     What  was  the 
candle  power  of  the  gas  flame  ? 

2.  If  a  plane  mirror  recedes  from  a  fixed  object  at  the  rate  of  10  ft.  a 
second,  at  what  rate  will  the  image  recede  from  the  mirror  ?    From  the 
object  ? 

3.  What  must  be  the  length  of  a  plane  mirror  in  order  that  an  observer 
may  see  his  whole  length  therein,  the  mirror  being  placed  parallel  to  the 
observer  ? 

4.  When  a  real  image  is  thrown  upon  a  screen  it  can  be  seen  from  all 
points  from  which  the  face  of  the  screen  can  be  seen.     When  the  image 
does  not  fall  upon  a  screen,  the  region  from  which  it  can  be  seen  is  much 
more  restricted.     Explain  this  difference  by  means  of  a  diagram  showing 
the  course  of  the  light  rays. 

5.  The  image  of  a  clock  face  is  thrown  upon  a  screen.     The  time  is 
12.30.    Make  a  diagram  of  the  image  as  seen  by  an  observer  looking  from 
the  lens. 

6.  In  a  photographic  camera,  using  a  single  lens,  let  the  plate  be  so 
placed  that  the  center  only  of  the  picture  is  distinct.     Must  the  plate  be 
pushed  nearer  the  lens  or  pulled  further  away  in  order  that  the  edges  of 
the  picture  may  become  distinct  ? 

7.  An  object  is  placed  at  a  distance  of  8cm  from  a  lens,  the  focal  length 
of  which  is  24cm ;  will  the  image  be  real  or  virtual  ?    Erect  or  inverted  ? 
At  what  distance  will  the  image  be  from  the  lens  ? 


244  EXPERIMENTAL   PHYSICS. 

8.  An  object  7cm  high  is  placed  at  a  distance  of  50cm  in  front  of  a  lens ; 
the  image  is  lcm  high ;  what  is  the  focal  length  of  the  lens  ? 

9.  At  what  distance  from  a  lens  must  an  object  be  placed  so  that  the 
image  shall  be  erect  and  twice  as  high  as  the  object  ? 

10.  An  object  placed  5cm  before  a  lens  has  its  image  formed  15cm  from 
the  lens  on  the  same  side ;  what  is  the  focal  length  of  the  lens  ? 

11.  An  object  placed  5cm  before  a  lens  has  its  image  erect  and  of  three 
times  its  linear  magnitude  ;  what  is  the  focal  length  of  the  lens  ? 

12.  A  candle  and  a  gas  flame  are  placed  180cm  apart.     If  the  gas 
flame  is  equivalent  to  four  candles,  where  must  a  screen  be  placed  on 
the  line  joining  the  candle  and  the  gas  flame,  in  order  that  it  may  be 
equally  illuminated  by  each  of  them  ? 

13.  Two  parallel  plane  mirrors,  A  and  B,  face  each  other  at  a  dis- 
tance of  5  ft.,  and  a  small  object  is  placed  between  them  at  a  distance  of 
2  ft.  from  J.,  and,  consequently,  3  ft.  from  B.     Calculate  the  distances 
from  A  of  the  two  nearest  images  that  are  seen  in  J.,  and  also  calculate 
the  distances  from  A  of  the  two  nearest  images  that  are  seen  in  B. 

14.  Two  plane  mirrors,  resting  in  a  vertical  position  upon  a  horizontal 
table,  make  an  angle,  A,  with  each  other.     A  ray  of  light  from  the  point 
P  strikes  one  of  the  mirrors  at  the  point  5,  whence  the  ray  is  reflected 
to  the  other  mirror  which  it  strikes  at  the  point  (7,  and  is  then  reflected 
in  the  direction  CQ.     Prove  that  the  angle  made  by  CQ  and  PB  is  two 
times  the  an.srlc  A . 


CHAPTER  VI. 

MECHANICS. 

106.  Mechanics   defined.     Mechanics   is  that  branch 
of  physics  which  deals   with  the  effects  of  force  upon 
matter.      Whenever  several  forces   act  upon  a  body  at 
rest,  one  of  two  things  happens,  either  the  body  remains 
at  rest,  or  else   the  body  moves.     For  convenience,  the 
subject  of  mechanics  is  divided  into  two  parts,  according 
as  the  forces  produce  rest  or  motion.     All  cases  of  forces 
producing  rest  are  grouped  under  the  head  of  statics,  while 
all  cases  where  motion  is  produced  are  grouped  under  the 
head  of  kinetics.     In  the   greater  part  of   this  chapter, 
experiments  in  statics  only  will  be  considered. 

107.  Mass;    Unit  of  Force;    Weight.     A  force  has 
already  been  denned  on  page  141  as  a  push  or  a  pull. 
Before  defining  the  unit  of  force,  which  we  shall  use  in 
a  good  deal  of  our  experimental  work,  it  will  be  well  to 
discuss  the  meaning  of  the  term  mass,  a  term  which  we 
shall  find  useful  in  defining  the  unit  of  force. 

The  mass  of  a  body  is  usually  defined  as  the  quantity  of 
matter  the  body  contains.  To  illustrate  this  definition  of 
mass,  suppose  two  pieces  of  iron  of  equal  size  and  alike 
in  every  particular  be  placed  together;  then  the  mass 
of  the  two  combined  will  be  twice  the  mass  of  either.  If 
three  pieces  of  iron  of  the  same  size  and  alike  in  every 
particular  be  placed  together,  the  mass  of  the  three  com- 
bined will  be  three  times  the  mass  of  any  one. 


246  EXPERIMENTAL    PHYSICS. 

The  study  of  physics  has  already  brought  before  us  the 
necessity  of  having  units  to  measure  various  quantities, 
as  length,  volume,  and  heat,  so  it  will  not  seem  strange 
to  look  about  for  some  unit  of  mass. 

There  is  a  piece  of  platinum  which  is  the  standard  for 
mass.  Copies  of  this  standard  have  been  made.  The  name 
of  this  unit  of  mass  is  the  pound.  In  a  grocery  shop  you 
may  see  lying  on  the  counter  pieces  of  iron  with  numbers 
upon  them.  These  pieces  of  iron  are  the  pounds  and 
multiples  and  fractions  of  the  pound.  They  have  been 
made  by  placing  one  of  the  standard  units  of  mass  in  one 
pan  of  a  balance  and  a  piece  of  iron  in  the  other  pan,  the 
piece  of  iron  being  filed  .till  it  just  balances  the  standard 
unit.  The  piece  of  iron  is  then  said  to  be  of  the  same 
mass,  that  is,  it  contains  the  same  amount  of  matter  as 
the  standard.  The  grocer  in  selling  his  goods  puts  one  of 
the  pieces  of  iron,  the  pound,  for  example,  into  one  pan 
of  the  balance  ;  into  the  other,  the  article  to  be  sold. 
When  a  sufficient  amount  of  the  article,  tea,  for  instance, 
is  put  into  the  pan,  the  unit  of  mass,  the  pound,  is  bal- 
anced by  the  tea.  Having  stated  what  the  unit  of  mass 
is,  the  unit  of  force  is  given  by  the  following : 

Definition.  The  unit  of  force,  the  pound,  is  the  pull  of 
the  earth  on  the  unit  of  mass,  the  pound. 

It  is  unfortunate  that  the  unit  of  force  has  the  same 
name  as  the  unit  of  mass. 

We  shall  measure  forces  by  means  of  the  spring  balance, 
an  instrument  made  of  a  spiral  spring  fastened  at  one  end 
to  a  support,  the  inner  side  of  the  frame  ;  at  the  other 
end  of  the  spring  is  a  little  index,  or  pointer,  which  moves 


REPRESENTATION    OF    FORCES.  247 

in  front  of  a  scale.  If  it  were  not  already  constructed,  we 
might  make  the  scale  of  the  balance  in  the  following  way : 
Upon  the  hook  of  the  balance  hang  a  mass  of  1  Ib.  Mark 
the  place  at  which  the  pointer  comes  to  rest.  Then  hang 
on  2  Ibs.,  and  mark  the  position  of  the  pointer.  Proceed 
in  this  way  till  the  scale  is  completed.  We  could,  if  we 
wished,  subdivide  the  pound  divisions  into  halves  and 
quarters,  and  thus  obtain  the  fraction  of  a  pound.  Would 
this  method  of  making  the  subdivisions  be  accurate  ?  (See 
Hook's  Law,  page  152.) 

Definition.  The  weight  of  a  body  is  a  force,  the  earth's 
putt  upon  the  body. 

NOTE.  The  word  "  weight ' '  as  commonly  used  is  ambiguous.  We  speak 
of  a  certain  weight  of  tea.  If  the  tea  has  been  weighed  with  a  spring 
balance,  the  use  of  the  word  "  weight"  in  the  preceding  sentence  is  cor- 
rect. (Why  ?)  On  the  other  hand,  if  a  beam  balance  (platform  balance) 
had  been  used,  the  use  of  the  word  "weight"  in  the  sentence  is,  strictly 
speaking,  incorrect.  (Why  ?) 

If  we  could  restrict  the  word  "  weighing"  to  the  operation  performed 
with  the  spring  balance,  and  could  use  the  word  "massing"  to  mean 
the  operation  performed  with  the  beam  balance,  what  would  be  the 
advantage  ? 

REPRESENTATION    OF    FORCES. 

1O8.  How  Forces  are  represented.  It  has  been  found 
convenient  to  represent  forces  by  straight  lines.  Thus  if 
a  force  of  5  Ibs.  is  made  to  act  in  a  northerly  direction 
upon  a  body,  mathematicians  represent  this  force  by  a 
straight  line  drawn  toward  the  north.  Then  to  show 
that  the  line  represents  a  force  of  5  Ibs.,  the  line  is  made 
five  times  the  length  of  a  line  representing  a  force  of  1  Ib. 
(The  length  of  the  line  representing  1  Ib.  is  chosen  at 
pleasure.) 


248 


EXPERIMENTAL    PHYSIOS. 


1O9.  Illustration  of  liow  a  Line  may  be  used  to 
represent  a  Force.  Let  us  suppose  a  line  0.5cm  long 
to  represent  in  magnitude  a  force  of 
1  Ib.  The  irregular  outline  of  Fig.  84 
representing  the  body,  the  line  AB, 
2.5cm  in  length,  drawn  toward  the  top 
of  the  page  represents  both  the  direc- 
tion of  the  force  and  also  its  magnitude, 
or  size.  It  is  convenient  to  indicate  the 
direction  in  which  a  force  acts  by  an 
arrowhead,  as  in  the  figure.  The  point 
B  of  the  body  at  which  the  force  is  ap- 
plied is  called  the  point  of  application 
of  the  force.  The  line  of  indefinite 
length,  of  which  AB  is  a  limited  por- 
tion, is  called  the  line  of  action  of  the 
force.  In  order  to  represent  completely 
a  force  on  paper,  three  things  must  be  known : 
(1)  The  magnitude  of  the  force  ; 

c  (2)    The   direction  of 

force ; 

(3)  The  point  of  application. 
The  line  AB  (Fig.  85)  represents  a  rod.  A  force 
of  5  Ibs.  applied  at  A  acts  downwards ;  a  force  of 
10  Ibs.  applied  at  (7,  the  middle  point  of  AB,  acts 
upwards ;  a  force  of  5  Ibs.  applied  at  B  acts  down- 
wards. 

In  representing  the  force  at  J.,  what  unit  of  length  has 
been  taken  to  represent  the  magnitude  of  1  Ib.  ? 


FIG.  84. 


the 


FIG.  85. 


HINT.     Measure  the  line  with  a  meter  stick. 


EQUILIBRIUM.  249 

Using  the  same  unit  of  length  to  represent  the  magni- 
tude of  a  force  of  1  Ib.  as  was  used  in  representing  the 
same  force  at  A,  draw  lines  to  represent  the  force  acting 
at  C  and  the  force  acting  at  B. 

EQUILIBRIUM. 

11O.  Conditions  of  Equilibrium.  Two  or  more  forces 
are  said  to  be  in  equilibrium,  or  to  balance,  when  they  are 
so  opposed  to  each  other  that  their  combined  action  on 
a  body  produces  no  change  in  its  rest  or  motion. 

To  determine  what  relation  must  exist  among  a  set  of 
forces  in  order  that  the  forces  may  neutralize  each  other 
in  their  action  on  a  body  to  which  they  are  applied  will 
be  our  immediate  task.  These  conditions  are  called  the 
conditions  necessary  for  equilibrium,  or,  more  briefly,  condi- 
tions of  equilibrium. 

The  purpose  of  the  next  experiment  is  to  find  the  con- 
ditions of  equilibrium  of  three  parallel  forces  whose  lines 
of  action  all  lie  in  one  plane,  and  whose  points  of  applica- 
tion lie  in  the  same  straight  line  which  is  at  right  angles 
to  the  line  of  action  of  the  forces. 

In  trying  to  discover  and  state  these  conditions,  the 
student  must  keep  in  mind:  (1)  the  magnitudes  of  the 
forces  under  consideration,  (2)  their  directions,  (3)  their 
points  of  application. 

There  are  various  forms  in  which  the  conditions  of 
equilibrium  may  be  stated;  one  of  these  forms,  good, 
although  not  the  most  concise,  consists  of  answers  to  the 
following  questions : 

(1)  How  does  the  magnitude  of  the  largest  force  compare 
with  the  sum  of  the  magnitudes  of  the  other  two  forces  ? 


250 


EXPERIMENTAL    PHYSICS. 


(2)  How  does  the  direction  of  the  largest  force  compare 
with  that  of  the  other  two  forces  ? 

(3)  What  is  the  position  of  the  point  of  application  of 
the    largest   force  with   respect   to   the   position    of   the 
points  of  application  of  the  other  two  forces? 

Experiment  1O3.  To  find  the  conditions  of  equilibrium 
of  three  parallel  forces  which  act  in  one  plane,  and  whose 
points  of  application  all  lie  in  the  same  straight  line. 

Apparatus.  Three  30-pound  spring  balances  ;  a  board  1  ft.  square 
protected  from  warping  by  pieces  fastened  to  the  edges  ;  the  top  of  this 
board  is  divided  into  squares  each  2  in.  on  a  side ;  at  the  corner  of 
each  is  a  hole,  and  the  holes  are  numbered  (Fig.  86)  from  1  to  49 
inclusive;  several  iron  pegs  to  fit  the  holes  rather  closely;  three 
marbles  equal  in  size ;  three  wooden  screws  with  attachments  to  fit 
the  edge  of  the  table;  supports  for  the  balances;  a  large  sheet  of 
common  window  glass. 

Directions.  On  the  top  of  a  table  lay  a  sheet  of  win- 
dow glass,  in  order  to  have  a  smooth  surface,  and  put  the 

marbles  on  the  glass  at  equal 
distances  from  one  another,  so 
that  they  shall  be  at  the  vertices 
of  an  equilateral  triangle.  Put 
a  peg  into  hole  27,  one  into  hole 
25,  and  one  into  hole  23.  Lay 
the  board,  marked  side  up,  on 
the  marbles.  At  one  end  of  the 
table  put  two  of  the  wooden 
screws,  as  shown  in  Fig.  87, 

JblG.   OD. 

fitting    them    to    the    table   by 

slipping  the  slot,  cut  in  the  piece  of  wood  attached  to  the 
screw,  over  the  edge  of  the  table.     When  attached  to 


EQUILIBRIUM. 


251 


the  table,  the  centers  of  these  pieces  through  which  the 
screws  pass  should  be  as  far  apart  as  the  holes  (23,  27) 
in  the  board  are  distant  from  each  other.  At  the  other 
end  of  the  table,  and  directly  opposite  the  portion  of  the 
table  midway  between  the  two  wooden  screws  already  in 
position,  place  the  remaining  wooden  screw.  Find  and 


FIG.  ST. 

record  the  correction  of  each  balance  (see  Exp.  58).  Place 
the  ring  of  a  spring  balance  over  the  hook  that  projects 
horizontally  from  the  top  of  the  little  nut  on  the  screw. 
Lay  the  spring  balance  on  its  back,  and  support  the  balance 
frame  near  each  end  by  little  pieces  of  wood,  as  shown  in 
the  figure.  In  like  manner  fasten  the  other  two  balances 
to  the  other  hooks,  and  support  them  in  the  little  rests. 
Have  the  nuts  near  the  ends  of  the  screws.  By  means 
of  strings,  not  doubled,  but  with  loops  in  their  ends,  attach 


252  EXPERIMENTAL   PHYSICS. 

• 

the  hooks  of  the  spring  balances  to  the  pegs  in  such  a  way 
that  the  strings  shall  be  parallel  to  each  other.  The  hooks 
of  the  balances  must  not  touch  the  board ;  the  strings  must 
not  press  down  on  the  edge  of  the  board ;  but  the  end  of 
each  string  which  passes  over  the  peg  must  rest  on  the 
board.  There  must  be  no  friction  in  any  of  the  balances. 
(Why?)  By  turning  the  screws,  the  strings  attached  to 
the  balances  can  be  brought  directly  over  the  lines  traced 
on  the  board  at  right  angles  to  the  line  in  which  the  pegs 
stand.  In  order  to  effect  this,  it  may  be  found  necessary 
to  move  one  of  the  screws  along  the  edge  of  the  table  for 
a  little  distance. 

When  this  adjustment  has  been  completed,  turn  the 
screws,  keeping  the  strings  over  the  proper  lines,  until 
the  balance .  attached  to  hole  25  registers  14  Ibs.,  when 
the  correction  for  the  error  due  to  its  horizontal  position 
is  taken  into  account.  In  all  work  involving  the  use  of 
one  or  more  spring  balances  in  the  horizontal  position,  a 
correction  must  be  applied  to  the  reading  of  each  spring 
balance. 

A  record  should  be  made  in  the  note-book  of  the 
magnitude  of  each  force,  its  direction,  and  its  point  of 
application.  For  ready  reference,  a  diagram  of  the  board 
should  be  made  in  the  note-book,  and  the  points  indicat- 
ing the  holes  should  be  numbered  from  1  to  49,  like  the 
holes  on  the  board.  A  brief  and  clear  record  can  be  made 
as  indicated  below : 

HOLE.  FORCE.  DIRECTION. 

23,     25,     27,  —      14,     -  V        i        V 


EQUILIBRIUM.  253 

The  space  on  each  side  of  the  14  should  be  filled  with 
the  numbers  representing  the  magnitudes  of  the  forces 
whose  points  of  application  are  at  23  and  27.  The  first 
arrow  indicates  the  direction  of  the  force  applied  at  23 ; 
the  second  arrow  that  of  the  force  at  25 ;  and  the  third 
arrow  that  of  the  force  at  27. 

Next,  having  slackened  the  balances,  take  the  peg  out 
of  hole  27  and  put  it  into  hole  26,  and  move  the  screw 
along  the  edge  of  the  table  till  it  is  opposite  hole  26. 
Proceed  as  before,  but  apply  a  force  of  15  Ibs.  to  the  peg 
at  hole  number  25.  Record  as  before. 

Slacken  the  spring  balances.  Take  the  peg  out  of  hole 
23  and  put  it  into  hole  22.  Move  the  screw  along  the 
edge  of  the  table  till  it  is  opposite  hole  22.  Apply  16  Ibs. 
to  the  peg  in  hole  25.  Record  as  before. 

Answer  the  following  questions : 

In  each  case,  how  does  the  magnitude  of  the  largest 
force  compare  with  the  sum  of  the  other  two  forces  ? 

What  is  the  direction  of  the  largest  force  as  compared 
with  the  direction  of  the  other  two  forces  ? 

Is  the  point  of  application  of  the  largest  force  always 
between  the  points  of  application  of  the  other  two  forces  ? 

Divide  the  greater  outside  force  by  the  smaller ;  also  the 
greater  distance  from  the  middle  force  by  the  smaller 
distance.  (The  "middle  force"  is  the  force  whose  point 
of  application  is  anywhere  between  the  two  outside  forces.) 

State  the  relation  between  the  two  outside  forces  and 
their  distances  from  the  middle  force. 

Divide  any  one  of  the  three  forces  in  one  of  the  groups 
by  either  of  the  other  forces.  Divide  the  distance  of  this 
last  chosen  force,  from  the  force  not  chosen,  by  the 


254  EXPERIMENTAL   PHYSICS. 

distance  of  the  first  chosen  force,  from  the  force  not 
chosen. 

State  the  relation  between  any  two  forces  and  their 
respective  distances  from  the  remaining  force. 

State  in  as  few  words  as  possible  the  three  conditions  of 
equilibrium  which  must  hold  in  order  that  any  group  of 
three  parallel  forces  may  balance. 

RESULTANT    AND    BQUILIBRANT. 

111.  Resultant  and  Equilibraiit  defined.  The  result- 
ant of  two  or  more  forces  is  a  single  force  that  will  exactly 
replace  them  in  its  action  on  a  body. 

Thus,  in  Exp.  103,  the  resultant  of  the  two  outside 
forces  in  any  case  would  be  a  force  which  has  the  same 
direction  as  the  two  outside  forces,  which  is  equal  to  their 
sum,  and  which  is  applied  at  the  peg  in  hole  25. 

The  resultant  of  one  of  the  outside  forces  and  the 
middle  force  would  be  a  force  equal  to  their  difference, 
applied  at  the  peg  to  which  the  other  outside  force  is 
applied,  but  in  the  opposite  direction,  that  is,  in  the  direc- 
tion of  the  greater  force. 

The  equilibrant  of  a  set  of  forces  is  a  single  force  that 
will  exactly  neutralize  their  action. 

Thus,  in  any  one  of  the  cases  of  Exp.  103,  the  middle 
force  is  the  equilibrant  of  the  two  outside  forces.  Either 
outside  force  is  the  equilibrant  of  the  middle  force  and  the 
other  outside  force. 

To  find  the  resultant  of  a  group  of  any  number  of 
parallel  forces,  we  must  replace  two  of  the  forces  by 
their  resultant,  then  replace  the  resultant  just  found 
and  one  of  the  remaining  forces  by  their  resultant,  and 


RESULTANT   AND   EQUTLIBRANT.  255 

proceed  in  this  manner  till  the  resultant  of  the  group  is 
obtained. 

The  special  name  of  couple  is  given  to  a  group  consist- 
ing of  two  parallel  forces,  equal  in  magnitude,  but  acting 
in  opposite  directions.  The  perpendicular  distance  be- 
tween the  lines  of  action  of  the  couple  is  called  the  arm 
of  the  couple.  The  effect  of  a  couple  is  to  rotate  the 
body  to  which  it  is  applied. 

EXAMPLES. 

1.  A  force  of  6  Ibs.  acts  due  north  and  a  force  of  15  Ibs.  acts  due 
south.     If  both  forces  have  the  same  point  of  application,  find  the  direc- 
tion and  magnitude  of  their  equilibrant ;  of  their  resultant. 

2.  A  rod  extends  east  and  west.     A  force  of  10  Ibs.  and  a  force  of 
5  Ibs. ,  both  acting  due  south,  are  applied  to  the  rod  at  points  6  ft.  apart. 
Find  the  equilibrant  of  the  two  forces  and  also  their  resultant,  stating 
the  direction,  magnitude,  and  point  of  application  of  the  equilibrant  and 
of  the  resultant. 

Solution.  From  the  conditions  of  equilibrium  which  we  have  found,  it 
follows  that  the  direction  of  the  equilibrant  must  be  due  north.  (Why  ?) 
It  also  follows  that  the  magnitude  of  the  equilibrant  must  be  10  -I-  5  =  15  Ibs. 
(Why  ?)  To  find  the  point  of  application  of  the  equilibrant,  a  little  more 
work  is  necessary.  From  the  remaining  ^ 

conditions  of  equilibrium,  if  C  (Fig.  88)  is 
the  point  of  application  of  the  equilibrant, 
we  have 

10  :  5  =  CB  :  CA. 
But  AB  =  6  ft. 

Consequently       CB  =  6  —  CA  ; 
hence  10  :  5  =  6  -  CA  :  CA. 

10  CA  =30-5  CA. 

15  (M  =  30. 

•'•  CA  =  2"  FIG.  88. 

Hence  CA  =  2  ft.,  that  is,  the  point  of  application  of  the  equilibrant 
is  2  ft.  from  the  point  at  which  the  force  of  10  Ibs.  is  applied. 

The  point  of  application  of  the  resultant,  as  well  as  its  magnitude,  is 
the  same  as  for  the  equilibrant,  but  its  direction  is  due  south.  (Why  ?) 


256  EXPERIMENTAL   PHYSICS. 

3.  A  rod  extends  east  and  west.     To  this  rod  a  force  of  15  Ibs.  is 
applied  due  north  and  5  Ibs.  due  south.     If  the  points  of  application  are 
9  ft.  apart,  find  the  direction,  magnitude,  and  point  of  application  of 
their  equilibrant ;  of  their  resultant. 

4.  To  a  rod  extending  east  and  west  are  applied  four  forces :  a  force 
of  5s  due  north,  a  force  of  10s  due  south,  a  force  of  15s  due  north, 
and  a  force  of  20s  due  south,  at  distances  of  10cm,  20cm,  30cm,  and 
40cm,  respectively,  from  the  western  end  of  the  rod.     Find  the  direc- 
tion, magnitude,  and  point  of  application  of  their  equilibrant;  of  their 
resultant. 

5.  A  rod  extending  east  and  west  is  acted  upon  by  a  force  of  20s  due 
north  and  by  a  force  of  20s  due  south.     If  the  points  of  application  are 
90cm  apart,  find  their  equilibrant. 

Solution.  The  two  forces  given  in  the  example  form  a  couple.  There 
is  no  single  force  that  will  balance  a  couple.  This  statement  may  be  bet- 
ter understood  by  the  student  after  examining  the  following  investigation : 

If  the  force  acting  toward  the  south  is  a  little  less  than  20s,  the 
equilibrant  will  be  a  small  force  acting  toward  the  south,  but  having  its 
point  of  application  a  long  distance  from  the  middle  force.  (Why  ?)  As 
the  force  acting  due  south  approaches  20s  as  its  limit,  the  equilibrant 
approaches  zero  as  its  limit,  and  its  point  of  application  moves  farther 
and  farther  away  along  the  line.  Hence,  mathematicians  say  that  the 
equilibrant  of  a  couple  may  be  regarded  as  a  zero  force  acting  at  an 
infinite  distance. 

6.  Find  the  directions,  magnitudes,  and  points  of  application  of  two 
forces  that  will  just  neutralize  the  tendency  of  the  pair  of  forces  given 
in  Example  5  to  rotate  the  rod. 

EQUILIBRIUM. 

112.  Points  of  Application  not  all  in  the  Same 
Straight  Line.  For  each  case  of  equilibrium  that  we 
have  tried,  the  points  of  application  of  the  forces  have 
been  in  a  straight  line,  which  was  perpendicular  to  the 
direction  of  the  forces.  In  Exp.  104  we  shall  examine 
cases  in  which  the  points  of  application  of  the  forces  are 
not  all  in  the  same  straight  line, 


EQUILIBRIUM.  Nsgf  CALlfO^  257 


Experiment  1O4.  To  find,  provided  three  given  parallel 
forces  are  in  equilibrium  when  their  points  of  application  lie 
in  the  same  straight  line,  whether  the  forces  will  sfyll  be  in 
equilibrium  when  their  points  of  'application  lie  ,  in  a  broken 
line. 

Apparatus.     The  same  as  in  Exp.  103. 

Directions.  Set  up  the  apparatus,  using  one  of  the 
cases  of  equilibrium  already  recorded  in  Exp.  103.  Then 
keeping  two  points  of  application  unchanged,  vary  the 
place  of  tlie  third  with  a  view  of  finding  any  positions  it 
may  have  such  that  when  the  forces  are  just  the  same  in 
magnitude  and  direction  as  at  first,  they  shall  still  be  in 
equilibrium.  Experiment  with  each  point  of  application 
in  turn,  and,  using  the  form  suggested  in  Exp.  103,  record 
the  result  of  the  trials  in  your  note-book. 

From  an  inspection  of  your  record,  what  inference  can 
you  draw? 

SUGGESTION.  If  points  are  found  at  which  the  forces  may  be  applied 
and  the  equilibrium  holds,  consider  how  these  points  are  situated  with 
respect  to  each  other  and  with  respect  to  the  line  in  which  they  at  first 
had  their  places. 

Experiment  1O5.  To  find,  provided  three  given  parallel 
forces  are  in  equilibrium,  whether  they  will  remain  in  equi- 
librium when  they  are  kept  parallel,  but  veered  round  in 
a  new  direction. 

The  question  we  wish  to  settle  may  be  made  a  little 
clearer  by  an  inspection  of  the  diagrams  on  the  following 
page. 


258 


EXPERIMENTAL   PHYSICS. 


/ 


FIG.  89. 


We  wish  to  find,  provided  the  forces  in  1  and  3  (Fig. 
89)  are  in  equilibrium,  whether  they  will  remain  in  equilib- 
rium when  veered  round  as  in  2  and  4. 

Apparatus.     The  same  as  in  Exp.  103. 

Directions.  Set  up  the  apparatus,  making  use  of  one  of 
the  cases  of  equilibrium  found  in  Exp.  103.  Then,  keep- 
ing the  magnitude  and  point  of  application  of  each  force 
unchanged,  veer  the  forces  round,  with  respect  to  the 
board,  into  a  new  direction,  but  keep  them  parallel  to 


MOMENT    OF   A    FORCE. 


259 


each  other.  The  easiest  way  to  veer  them  round  is  to 
tighten  one  of  the  screws,  and  to  loosen  the  others  till 
the  strings,  remaining  parallel  to  each  other,  no  longer 
lie  along  the  lines  traced  upon  the  board.  Record  the 
trials  and  the  results  in  your  note-book. 

What  conclusion  do  you  draw  from  the  experiment  as 
thus  far  performed? 

Repeat  the  experiment,  using  any  case  of  equilibrium  to 
begin  with  found  in  Exp.  104,  where  the  points  of  appli- 
cation do  not  lie  in  the  same  straight  line.  Record  the 
trials  and  the  results. 

Do  you  find  the  same  result  as  in  the  first  part  of  the 
experiment  ? 

What  general  conclusion  can  you  draw  from  this  experi- 
ment? 

MOMENT    OF   A   FORCR 

113.    Definition  of  the  Moment  of  a  Force.     Before 
discussing   the  record  of   the  results  of 
Exp.  105,  we  will  define  the  meaning  of 
the  term  moment  of  a  force. 

The  moment  of  a  force  is  the  power  the 
force  has  to  rotate  the  body,  to  which  it  is 
applied,  about  some  selected  axis.  This 
power  depends  not  only  upon  the  magni- 
tude of  the  force,  but  upon  its  position. 

A  force  applied  to  the  middle  of  a  door 
has  less  power  to  turn  the  door  on  its 
hinges  than  if  it  were  applied  to  the  side 
of  the  door  remote  from  the  hinges.  The 
"  selected  axis  "  in  this  case  is  the  line  FIG.  90. 


260  EXPERIMENTAL    PHYSICS. 

running  through  the  hinges  about  which  the  door  turns, 
as  shown  in  Fig.  90. 

Definition.  The  numerical  measure  of  the  moment  of  a 
force,  with,  respect  to  an  axis,  is  the  product  of  the  force  and 
the  perpendicular  let  fall  on  its  line  of  action  from  the  axis. 

Let  the  irregular  outline  represent  a  body ;  let  a  force, 
F,  act  on  the  body  in  the  plane  of  the  paper;  let  an  axis, 
perpendicular  to  the  paper,  pierce  it  at  0.  Then  the 

moment  of  the  force,  F,  about 
the  axis  through  the  body  at 
0  is  F  X  OM,  where  OM  is  the 
length  of  the  perpendicular  let 
fall  from  0  upon  the  line  of 
action  of  F. 

Now  work  out  in  vour  note- 

FlG.  91.  J 

book    the    moments    for    two 

cases  of  equilibrium  in  Exp.  103,  for  two  cases  in  Exp. 
104,  and  for  two  cases  (if  you  found  as  many)  in  Exp.  105. 
In  each  case  take  in  turn  for  the  axis  each  of  the  three 
pegs  used  in  that  case,  and  at  least  one  other  peg.  This 
will  make  twelve  moments  calculated  for  each  case  of 
equilibrium.  The  calculations,  however,  are  extremely 
simple.  Call  a  moment  positive  if  it  tends  to  produce 
rotation  round  the  given  axis  in  the  direction  of  the  motion 
of  the  hands  of  a  watch.  Call  a  moment  negative  if  it 
tends  to  produce  rotation  in  the  opposite  direction  round 
the  axis. 

Is  there  anything  in  the  nature  of  the  case  why  we 
should  regard  one  direction  of  rotation  positive  rather 
than  the  other? 


MOMENT    OF    A    FORCE. 


261 


We  can  now  replace  the  set  of  three  conditions,  for  the 
equilibrium  of  parallel  forces,  suggested  on  pages  249  and 
250  by  a  set  of  two  conditions  only : 

(1)  The  algebraic  sum  of  the  forces  must  be  zero ;  that 
is,  the  sum  of  the  forces  in  one  direction  must  be  equal  to 
the  sum  of  the  forces  in  the  opposite  direction. 

(2)  The  algebraic  sum  of  the  moments  of  the  forces 
must  be  zero;  that  is,  the  tendency  for  rotation  in  one 
direction  must  be  equal  to  the  tendency  in  the  opposite 
direction. 

NOTE.  The  algebraic  sura  of  two  or  more  quantities  is  the  result 
obtained  by  adding  them  according  to  the  rules  of  algebra,  which  take 
into  account  the  signs  of  the  quantities. 

The  set  of  conditions  given  above  is  true  for  the  equi- 
librium of  any  number  of  parallel  forces  in  one  plane. 
To  illustrate  the 
applications  of  the 
conditions  of  equi- 
librium just  stated, 
let  us  find  the  equi- 
librant  of  the  set  of 
forces  described  in 
Fig.  92,  and  conse- 
quently the  result- 
ant which  always 
has  the  same  mag- 
nitude as  the  equi- 


M 


12 


10 


FIG.  92. 


librant,    but   the 
opposite  direction. 

We  will  call  forces  acting  upwards  positive,  and  those 
acting  downwards  negative, 


262 


EXPERIMENTAL    PHYSICS. 


The  distance  KL  —  LM=  2,  and  MN=  NO  =  4. 

Making  use  of  condition  (1),  that  is,  in  order  to  have 
equilibrium,  the  algebraic  sum  of  the  forces  acting  on  a 
body  must  be  zero,  we  find,  x  being  the  magnitude  of  the 
equilibrant, 

x  —  6  +  8  —  1  0  +  1  2  =  0  ,  or  x  =  —  4  . 


12 


The  magnitude  of 
the  equilibrant 
is  then  4.  The 
minus  sign  denotes 
that  the  equili- 
brant acts  down- 
M_  _  |  _  o  wards.  (Why  ?) 

To  make  use  of 
condition  (2),  let 
us  first  calculate 
the  moments  with 

10  respect  to  an  axis 

passing    through 
K. 

Moment  of    6  about  K=        (6x0)  =  0. 
"        "     8      "      "=    —(8x2)  =  —  16. 
"         "  10      "      "  =      (10  X  4)  =  40. 
"        "12      «      «  =—  (12  x  8)  =  —  96. 
Moment  of  the  equilibrant,  4,  at  the  unknown  distance  y 
from  K  =  4  X  y=  ty* 

Hence,  4y  +  0  —16  +  40  —  96  =  0,  or  4y  =  72. 
Hence,  y  =  18  units  to  the  right  from  K.     Why  is  not 
the  distance  18  units  to  the  left  from  J5T? 

We  see  that  the  first  condition  gives  us  the  direction 


MOMENT    OF    A    FORCE.  263 

and  magnitude  of  the  equilibrant ;  the  second  condition, 
the  point  of  application  of  the  equilibrant. 

Let  us  now  take  moments  about  M,  that  is,  apply  the 
second  condition  with  respect  to  an 'axis  through  M. 
Moment  of    6  about  M=     -(G  X  4)  =  —  24. 
«     8      "       "  =        (8x2)  =  16. 
"  10      "       «•  —      (10  X  0)  =  0. 
"12      "       "=  — (12  X4)  =  — 48. 

Moment  of  the  equilibrant,  4,  at  the  unknown  distance 
z  from  M=  4  X  z  =  4z. 

Then  4z  —24  +  16  +  0  —48  =  0,  or  4z  =  56. 

Hence,  z  =  14,  that  is,  the  point  of  application  of  the 
equilibrant  is  14  units  to  the  right  from  M ;  but  14  to 
the  right  from  Mis  equal  to  18  to  the  right  from  K,  so  the 
result  reached  is  the  same  as  before. 

Compute  the  moments  about  0. 

Will  the  direction,  the  magnitude,  and  the  point  of 
application  of  the  resultant  of  the  four  forces  be  the  same, 
no  matter  what  point  is  taken  to  pass  an  axis  through 
about  which  to  compute  moments  ? 

Experiment  1O6.  To  find  what  relations  must  exist 
among  four  forces  (one  acting  north,  one  south,  one  east, 
one  west)  in  one  plane,  in  order  that  they  may  be  in 
equilibrium. 

Apparatus.  The  same  as  in  Exp.  103,  but  with  one  more  spring 
balance. 

Directions.  Perform  this  experiment  on  a  wide  table. 
With  the  four  spring  balances,  each  pulling  in  a  different 
direction,  but  always  along  some  line  marked  on  the  board, 
as  shown  in  Fig.  93,  make  three  cases  of  equilibrium. 


264 


EXPERIMENTAL    PHYSICS. 


Take  new  points  of  application  and  new  magnitudes  of 
forces  for  each  case.  Record  in  a  manner  similar  to  that 
suggested  in  Exp.  103. 

In  each  case,  is  there  any  fixed  relation  between  the 
magnitude  of  a  force  acting  in  one  direction  and  the  mag- 
nitude of  a  force  acting  in  the  opposite  direction  ? 

Selecting  one  of  the  cases  of  equilibrium  you  have 
made,  compute  the  moments  of  its  forces  with  respect  to 

one  of  the  pegs  used  in  this  case. 
Then  for  this  same  case  make 
three  more  computations,  one  with 
respect  to  each  of  the  three  re- 
maining pegs.  Finally,  compute 
for  this  case  the  moments  of  its 
forces  about  some  peg  put  at  ran- 
dom into  any  hole  in  the  board. 

In  each  set  of  moments  thus 
computed,  does  the  algebraic  sum 
of  the  moments  equal  zero  ? 

Calling  forces  acting  east  positive,  those  acting  west 
negative,  forces  acting  north  positive,  those  acting  south 
negative,  state  carefully  two  general  laws  modeled  after 
those  given  on  page  261. 

QUESTIONS.  When  any  number  of  forces  are  acting  upon  a  pivoted 
body,  what  is  the  necessary  condition  for  their  causing  no  rotation  ? 
When  a  body  is  subjected  to  forces  acting  in  one  plane  only,  what  con- 
ditions must  be  fulfilled  in  order  that  the  body  may  neither  slide  nor 
turn? 

GRAVITY. 

114.  Center  of  Gravity.  The  earth  pulls  downward 
on  each  of  the  many  particles  of  which  a  body  is  com- 


FlG.  93. 


GRAVITY.  265 

posed.  This  downward  pull  of  the  earth  is  called  gravity. 
In  the  next  experiment  we  shall  take  as  the  body  to  be 
considered  a  piece  of  cardboard.  Since  the  cardboard  is 
composed  of  a  great  number  of  particles,  there  are  a  vast 
number  of  forces  acting  downward  upon  the  body.  All 
these  forces  are  practically  parallel.  (Why?)  The  object 
of  the  experiment  is  to  find  whether  the  resultant  of  these 
parallel  forces  passes  through  a  fixed  point  about  which 
the  cardboard  will  balance,  if  supported  at  this  point. 

Experiment  1O7.  To  find  the  center  of  gravity  of  a 
piece  of  cardboard  of  triangular  shape. 

Apparatus.  A  triangle  of  cardboard  whose  sides,  for  example, 
are  10cm,  20cm,  and  25cm  long ;  a  piece  of  thread ;  a  pin ;  a  bit  of 
sheet  lead. 

Directions.  Through  the  cardboard,  very  near  one 
corner,  stick  a  pin,  and  enlarge  a  little  the  •  hole  thus 
made,  so  that  when  the  pin  is  stuck  horizontally  into  the 
edge  of  the  table,  the  cardboard  will  swing  freely  with  but 
little  friction  at  the  hole.  When  the  card- 
board, thus  suspended,  comes  to  rest,  "  the 
resultant  force  of  its  weight  is  balanced 
by  the  upward  elastic  resistance  to  bending 
exerted  by  the  pin ;  and  a  plumb  line,  made 
of  a  bit  of  lead  fastened  to  the  end  of  a 
piece  of  thread,  hung  over  the  pin,  will 
give  the  direction  in  which  either  force 
acts."  Hang  the  plumb  line  over  the  pin 
by  a  loop,  as  shown  in  Fig.  94.  Have  the  plumb  line  long 
enough  to  reach  more  than  across  the  cardboard.  Mark 
the  point  where  the  plumb  line  crosses  the  lower  edge  of 


266  EXPERIMENTAL    PHYSICS. 

the  cardboard.  Now  take  down  the  cardboard  and  draw 
on  it,  with  a  sharp-pointed  lead-pencil,  a  line  from  the  pin 
hole  to  the  point  where  the  plumb  line  crosses  the  edge  of 
the  cardboard;  this  line,  thus  drawn,  gives  the  direction 
of  the  resultant  force  of  gravity  on  the  cardboard. 

Hang  the  cardboard  from  another  corner,  and  repeat  the 
process.  A  second  line  for  the  direction  of  the  resultant 
force  of  gravity  is  thus  obtained.  Call  the  point  in  which 
the  second  line  cuts  the  first  one,  G-.  Now  suspend  the 
cardboard  from  its  third  angle. 

Does  the  plumb  line  cross  the  point  G-  ? 

Lay  the  cardboard  in  a  horizontal  position  on  a  pin- 
point, so  that  G-  shall  rest  upon  the  pin-point. 

Does  the  card  balance  ? 

Does  the  resultant  of  all  the  parallel  forces  constituting 
the  weight  of  a  body  pass  through  a  fixed  point  ? 

Why  is  this  point  called  the  "  center  of  gravity  "  ? 

Does  the  center  of  gravity  of  the  piece  of  cardboard  lie  on 
one  of  the  surfaces,  or  midway  between  the  two  surfaces  ? 

Can  we  regard  the  weight  of  a  body  as  collected  at  its 
center  of  gravity  (that  is,  if  we  could  replace  all  the  paral- 
lel forces  which  constitute  the  weight  of  the  body  by  a 
single  force  equal  to  the  sum  of  this  great  number  of 
parallel  forces,  would  the  line  of  action  of  this  single 
force  pass  through  the  center  of  gravity  of  the  body)  ? 

This  question  we  shall  try  to  answer  in  the  next 
experiment. 

Experiment  1O8.  To  find  whether  the  weight  of  a  body 
acts  just  as  if  it  were  all  collected  at  the  center  of  gravity  of 
the  body. 


GRAVITY.  267 

Apparatus.     A  wooden  stand  like  that  used  in  Exp.  24  ;  a  heavy 
iron  ball ;  a  triangular  prism  of  wood ;  a  30-pound  spring  balance. 

Directions.  Record  the  weight  of  the  ball  in  pounds, 
and  also  that  of  the  stand.  On  a  table,  near  the  corner, 
lay  the  triangular  piece  of  wood,  and  on  this  lay  the  stand 
(Fig.  95)  to  which  the 
iron  ball  is  hung  by  a 
loop  of  string.  Have  ^  ^ 
the  edge,  not  the  face,  I 

of    the    meter   stick,  Jk 

which  is  fastened  to 

,  ,  ,  FIG.  95. 

the  stand,  rest  on  the 

triangular  piece  of  wood.  On  the  triangular  piece  of  wood 
balance  the  stand  with  the  weight  attached.  Then  record 
the  distance  from  the  end,  A  (Fig.  95),  to  the  point  of 
application,  P,  of  the  weight;  also  record  the  distance 
from  A  to  the  fulcrum,  8. 

What  is  the  distance  in  centimeters  from  P  to  SI 
Considering  the  weight  of  the  ball  as  one  downward 
force,  and  the  weight  of  the  stand,  the  body,  as  the  other 
downward  force,  find,  by  applying  the  principle  of  moments, 
at  what  distance  from  the  fulcrum,  S,  the  weight  of  the 
stand,  if  collected  at  one  point,  would  have  to  be  applied  in 
order  to  produce  the  state  of  equilibrium  that  is  observed. 
Apply  the  principle  of  moments  in  the  following  way: 
Multiply  the  weight  of  the  ball  by  its  distance  from  the 
fulcrum  ;  also,  denoting  by  x  the  distance  from  the  ful- 
crum to  the  point  where  the  weight  of  the  stand  would 
have  to  be  collected  in  order  to  produce  the  state  of  equi- 
librium observed,  multiply  the  weight  of  the  stand  by  x. 
Put  the  two  products  thus  obtained  equal  to  each  other 


268  EXPERIMENTAL    PHYSICS. 

(we  have  a  right  to  do  this  by  the  second  condition  of 
equilibrium,  page  261),  and  solve  the  equation  thus  ob- 
tained to  get  the  value  of  x.  Add  to  x  the  distance,  SA, 
from  the  fulcrum  to  the  end,  A,  of  the  stand. 

What  is  the  distance  from  A  of  the  point  obtained  by 
this  computation? 

Now  change  the  position,  P,  of  the  ball  on  the  stand,  and 
balance  again.  Make  measurements  and  record  as  before. 

What  is  the  distance  from  A  of  the  point  obtained  by 
this  computation? 

Finally,  remove  the  ball,  and  balance  the  stand  alone 
on  the  triangular  piece  of  wood. 

What  is  the  distance  in  centimeters  from  the  end,  A,  to 
the  balancing-point,  the  center  of  gravity,  the  present 
position  of  the  fulcrum? 

How  does  the  distance  just  obtained  compare  with  the 
two  computed  distances  from  A  ? 

Has  or  has  not  the  weight  of  the  stand  acted  as  if 
collected  at  the  center  of  gravity? 

How  great  a  pressure  has  been  exerted  upon  the  sup- 
port, that  is,  upon  the  triangular  piece  of  wood,  in  each  of 
the  three  oases? 

Can  you  always  regard  the  weight  of  a  body  as  a  force 
applied  at  the  center  of  gravity  of  the  body? 

How  could  you  find,  by  applying  the  teachings  of  this 
experiment,  the  weight  of  the  stand,  if  the  position  of  its 
center  of  gravity,  the  position  of  the  fulcrum,  the  position 
of  the  iron  ball,  and  also  the  weight  of  the  iron  ball  Avere 
given  ? 

How  could  you  find  by  experiment  the  center  of  gravity 
of  the  stand? 


GRAVITY.  269 


EXAMPLES. 

1.  A  uniform  straight  lever  10  ft.  long  balances  at  a  point  3  ft.  from 
one  end,  when  12  Ibs.  are  hung  from  this  end  and  an  unknown  weight 
from  the  other.    The  lever  itself  weighs  8  Ibs.    Find  the  unknown  weight. 

Solution.  Denoting  by  x  the  unknown  weight  in  pounds,  and  regard- 
ing the  weight  of  the  lever  as  a  force  applied  at  its  center  of  gravity,  take 
moments  about  the  point  of  support  thus : 

12  X  3  —  8  X  2  +  x  X  7, 
or  7z  =  36  -  16  =  20. 

.-.  x  =  2f. 

Hence,  the  weight  which  was  to  be  found  is  2f-  Ibs. 

NOTE.  Whenever  we  say  a  lever  is  uniform,  we  mean  that  its  center 
of  gravity  is  the  center  of  its  length. 

2.  A  straight  lever  6  ft.  long  weighs  10  Ibs.,  and  its  center  of  gravity 
is  4  ft.  from  one  end.     What  weight  at  this  end  will  support  20  Ibs.  at 
the  other,  when  the  lever  is  supported  at  a  distance  of  1  ft.  from  the  end 
nearer  the  center  of  gravity  ? 

3.  A  telegraph  pole  is  made  of  three  hollow  iron  cylinders  joined  end 
to  end.     Each  cylinder  is  4m  long;  the  lowest  weight  250ks,  the  middle 
one  150ke,  and  the  uppermost  50ks.     Find  the  center  of  gravity  of  the 
pole. 

SUGGESTIONS.  Regard  the  weight  of  each  section  as  applied  at  the 
center  of  gravity  of  the  section  to  which  it  belongs.  Imagine  the  pole 
placed  in  a  horizontal  position.  Find  where  a  prop  would  have  to  be 
placed  to  produce  equilibrium. 

4.  A  cube  of  wood,  10cm  on  each  edge  and  of  specific  gravity  0.5,  is 
covered  on  one  side  by  a  plate  of  metal  10cm  square,  lcm  thick,  of  specific 
gravity  5.     How  far  from  the  outer  surface  of  the  metal  plate  is  the 
center  of  gravity  of  the  whole  ? 

5.  Two  uniform  cylinders  of  the  same  diameter,  whose  lengths  are  1  ft. 
and  7  ft.,  respectively,  and  whose  weights  are  in  the  ratio  of  5  to  3,  are 
joined  together  so  as  to  form  one  cylinder.     Find  the  position  of  the 
fulcrum  about  which  the  whole  will  balance. 


270  EXPERIMENTAL   PHYSICS. 


LEVERS. 

115.  Classes  of  Levers.  A  lever  is  a  rod,  or  bar,  by 
means  of  which  a  force  can  be  applied  more  advanta- 
geously than  it  otherwise  could  in  moving  a  body.  A 
crowbar  is  a  lever.  It  is  rested,  near  one  end,  on  a  piece 
of  stone  or  other  firm  support,  called  a  fulcrum.  The  end 
near  the  fulcrum  is  placed  under  the  body  to  be  raised, 
and  a  force  is  applied  at  the  other  end  tending  to  bring 
this  end  downward.  The  body  to  be  moved  is  called  the 
weight,  and  the  force  applied  at  the  other  end  of  the  crow- 
bar is  called  the  power.  There  are  three  classes  of  levers. 
A  lever  like  the  one  just  described,  where  the  fulcrum  is 
between  the  weight  and  the  power,  is  called  a  lever  of  the 
first  class. 

An  oar,  when  used  in  rowing  a  boat,  is  a  lever.  The 
water  into  which  the  blade  of  the  oar  dips  is  the  fulcrum, 
the  resistance  of  the  boat  to  being  urged  forward  is  the 
weight,  which  meets  the  oar  at  the  rowlock,  and  the  force 
of  the  rower's  arm  is  the  power.  When  the  weight  is 
between  the  fulcrum  and  the  power,  as  in  the  case  of  an 
oar,  the  lever  is  called  a  lever  of  the  second  class. 

A  pitchfork,  when  used  in  lifting  hay,  is  a  lever.  One 
end  is  held  firmly  in  the  hand,  which  is  the  fulcrum,  the 
hay  at  the  other  end  is  the  weight,  and  the  force,  applied 
by  the  other  hand  to  the  pitchfork  somewhere  between 
the  fulcrum  and  the  weight,  is  the  power.  When  the 
power  is  between  the  fulcrum  and  the  weight,  the  lever  is 
called  a  lever  of  the  third  class. 

In  many  problems  concerning  levers,  the  weight  and 
the  power  are  supposed  to  act  at  right  angles  to  the  lever, 


NON-PARALLEL   FORCES.  271 

and  the  distance  measured  along  the  lever  from  the  ful- 
crum to  the  weight  is  called  the  weight-arm,  while  the 
distance  from  the  fulcrum  to  the  power  is  called  the  power- 
arm.     By  applying  the  principle  of  moments  we  have : 
power  X  power-arm  =  weight  X  weight-arm. 

QUESTIONS.  Which  is  the  greater,  the  power  or  the  weight  in  a  lever 
of  the  first  class  ?  In  a  lever  of  the  second  class  ?  In  a  lever  of  the 
third  class  ? 

NON-PARALLEL   FORCES. 

116.  Concurrent  Forces.  We  have  given  consider- 
able study  to  cases  of  equilibrium  where  we  have  had 
three  parallel  forces  acting  on  a  body,  and  we  have  found 
the  resultant  and  the  equilibrant  of  groups  of  parallel 
forces. 

It  now  remains  for  us  to  study  the  conditions  of  equi- 
librium of  three  concurrent  forces,  that  is,  forces  whose 
lines  of  action  meet  in  a  point. 

Experiment  1O9.  To  find  the  condition  for  equilibrium 
of  three  concurrent  forces. 

Apparatus.  Three  30-pound  spring  balances ;  two  pieces  of  slen- 
der, strong,  hard-twisted  string  70cm  or  80cm  long ;  a  wooden  block 
like  the  one  whose  specific  gravity  you  found ;  a  meter  stick. 

Directions.  The  experiment  is  to  be  performed  on 
a  table  with  a  smooth  top.  Note  the  error  of  each  bal- 
ance when  in  the  horizontal  position.  Tie  a  loop  in  each 
end  of  one  string.  Do  the  same  to  the  other  string, 
only  make  one  of  the  loops  10cm  long.  Pass  the  first- 
mentioned  string  through  the  large  loop,  so  that  the  large 
loop  lies  between  the  loops  in  the  ends  of  this  string,  each 
of  which  loops  should  be  slipped  on  the  hook  of  a  spring 


272 


EXPERIMENTAL   PHYSICS. 


balance,  one  loop  only  on  one  hook.  The  spring  balances 
should  be  kept  in  place  by  having  their  rings  fastened  to 
the  screws  in  blocks  clamped  near  two  corners  of  the 
table,  shown  in  Fig.  96,  but  the  balances  should  be  able 
to  swing  freely  round  the  screws  in  any  horizontal  posi- 
tion. Slip  the  remaining  loop  of  the  second  string  over 


FIG.  96. 

the  hook  of  the  remaining  spring  balance.  Now  pull  the 
third  spring  balance  by  its  ring  in  any  desired  direction 
and  with  such  a  force  as  to  draw  the  strings  tight,  and 
make  each  balance  point  in  the  same  direction  as  the 
string  attached  to  its  hook.  By  means  of  a  clamp,  fasten 
the  balance  by  its  ring.  Make  a  careful  reading  of  each 
balance,  taking  care  to  apply  the  proper  correction  to 
each.  Put  the  open  note-book  beneath  the  junction  of 
the  strings,  and  on  the  page,  with  the  block  as  a  guide, 


TRIANGLE   OF    FORCES.  273 

draw,  with  a  sharp  lead-pencil,  a  line  a  few  centimeters  in 
length  parallel  to  each  string  and  beneath  it.  From  the 
point  where  these  lines  meet,  when  produced  if  necessary, 
lay  off  on  each  line  an  arrow  proportioned  in  length  to  the 
reading  of  the  balance  whose  pull  was  directed  along  the 
line,  the  tip  of  the  arrow  in  each  case  pointing  away  from 
the  junction.  From  the  tip  of  any  arrow  lay  off  a  line 
parallel  and  equal  to  one  of  the  other  arrows,  and  from 
the  end  of  the  line  thus  drawn  draw  another  line  parallel 
and  equal  in  length  to  the  remaining  arrow.  (It  is  not 
impossible  that  the  line  last  drawn  will  coincide  with  the 
line  to  which  it  is  drawn  parallel.) 

What  is  the  name  of  the  geometrical  figure  formed  by 
the  two  lines  just  drawn  and  the  selected  arrow. 

Point  out  how  the  following  statement  agrees  with  the 
result  of  the  experiment: 

If  three  forces  acting  upon  a  material  point  are  in  equi- 
librium, and  three  lines  be  drawn,  without  taking  the 
pencil  off,  parallel  to  the  successive  forces  acting  on  the 
point  and  in  the  same  direction  with  them,  and  propor- 
tional to  them  in  magnitude,  a  triangle  will  be  formed. 

The  triangle  thus  formed  is  called  the  triangle  of  forces. 

If  the  three  forces  are  not  in  equilibrium,  the  lines  will 
not  form  a  triangle. 

TRIANGLE    OP   FORCES. 

117.  Principle  of  the  Triangle  of  Forces.  If  three 
forces  are  in  equilibrium,  and  any  triangle  be  drawn  with 
its  sides  parallel  to  the  lines  of  action  of  the  forces,  the 
lengths  of  these  sides  will  represent  the  relative  magni- 
tudes of  the  corresponding  forces. 


274 


EXPERIMENTAL    PHYSICS. 


Test  the  statement  just  made  by  drawing  a  triangle  on 
the  page  of  your  note-book,  the  sides  of  the  triangle  being 
drawn  parallel  to  the  direction  of  the  forces  recorded  in 
Exp.  109. 

On  two  of  the  arrows,  in  your  original  figure,  as  sides, 
construct  a  parallelogram.  Produce  the  remaining  arrow 
backwards  by  its  own  length  from  the  point  whence  the 
three  original  arrows  spring. 

Does  the  line  you  have  just  drawn 
coincide  or  nearly  coincide  with  the 
diagonal  of  the  parallelogram  ? 

In  the  case  of  three  concurrent 
forces,  as  A,  B,  and  C  of  Fig.  97,  in 
equilibrium,  we  have  the  following 
relations : 

A  is  the  equilibrant  of  B  and  C. 
B  "  "  "  "  A  "  C. 

C  "  "  "  "  A  "  B. 

a  "    "     resultant     "  B    "     0. 

b  "    "  "  "  A    "     C. 

c  "    "  "  "  A    "    B. 

QUESTIONS.  What  is  the  condition  that  must  hold  in  order  that  three 
concurrent  forces  shall  be  in  equilibrium  ? 

A  force  of  10  Ibs.  acts  due  east,  and  a  force  of  10  Ibs.  acts  due  north, 
at  the  same  point.  What  is  the  magnitude  of  their  resultant  ?  Of  their 
equilibrant  ?  In  what  direction  does  the  resultant  act  ? 


EXAMPLES. 

1.  A  ball,  of  weight  2  Ibs.  and  of  radius  4  in.,  is  suspended  by  a  string 
fastened  to  a  vertical  wall.  The  ball  rests  against  the  wall,  and  the  direc- 
tion of  the  string  passes  through  the  center  of  the  ball.  If  the  distance 
of  the  point  at  which  the  string  is  fastened  to  the  wall  is  6  in.  above  the 


EXAMPLES.  275 

point  where  the  ball  touches  the  wall,  find  the  pressure  of  the  ball  against 
the  wall. 

Solution.  In  Fig.  98  let  P  be  the  point  at  which  the  end  of  the  string 
is  fastened  to  the  wall  ;  let  M  be  the  point  at  which  the  ball  touches  the 
wall.  We  are  asked  to  find  the  pressure  of  the  ball 
against  the  wall.  This  pressure  will  be  equal  to  the 
push  of  the  wall  against  the  ball.  There  are  three 
forces  which  keep  the  ball  in  equilibrium,  the  weight 
of  the  ball,  the  push  of  the  wall,  and  the  tension  of 
the  string;  but  these  three  forces  pass  through  a 
single  point,  C,  so  let  us  denote  the  weight  by  CW, 
the  push  by  CjR,  and  the  tension  by  CT.  These 
three  forces  are  in  equilibrium,  and  are  parallel, 
respectively,  to  PM,  JfO,  and  CP,  the  sides  of  the 
right  triangle,  PMC.  Hence,  by  the  principle  of  the  triangle  of  forces, 

CW  =  PM 
CR       MG' 

By  the  conditions  of  the  problem,  CW  =  2  Ibs.,  PM  =  6  in.,  and 
MG  =  4  in.,  consequently,  if  we  denote  by  x  the  required  force,  CR, 

2  _6 

z~4 


Hence,  the  pressure  of  the  ball  against  the  wall  is  1.33  Ibs. 

2.  Find  the  tension  of  the  string  in  Ex.  1. 

3.  A  picture  frame  weighing  10  Ibs.  is  hung  by  a  cord  passing  over 
a  nail,  the  two  parts  of  the  cord  making  an  angle  of  90°  with  each  other. 
Find  the  tension  in  the  cord. 

4.  A  uniform  pendulum  rod  is  pulled  aside  from  the  vertical  by  a 
horizontal  force  applied  to  the  lower  end.     If  the  pendulum  rod  weighs 
10s,  what  must  be  the  horizontal  force  in  order  that  the  pendulum  rod, 
when  in  equilibrium,  shall  make  an  angle  of  45°  with  its  former  position  ? 

5.  An  isosceles  triangle,  the  vertical  angle  of  which  is  equal  to  120°, 
is  drawn  on  a  vertical  wall  with  its  base  horizontal  and  its  vertex  down- 
wards.    At  each  corner  of  the  triangle  a  smooth  peg  is  driven  into  the 
wall  at  right  angles.     A  thread  with  12s  attached  to  each  end  is  passed 
under  the  lower  peg  and  over  the  other  two  pegs.     Find  the  pressure  on 
each  peg.    Find  also  the  vertical  and  the  horizontal  pressure  on  each  peg. 


276 


EXPERIMENTAL    PHYSICS. 


COMPOSITION    AND    RESOLUTION. 

118.    Composition  and  Resolution  of  Forces.      The 

process  of  finding  the  resultant  of  a  group  of  forces  is  called 

the  composition  of  forces,  while 
the  process  of  finding  two 
forces  which  will  exactly  re- 
place a  single  force  in  its  action 
upon  a  body  is  called  the  reso- 
lution of  forces. 

In  the  composition  of  forces 
we  get  one  definite  answer  to 
the  problem. 

In  the  resolution  of  forces 
we  get  an  _  indefinite  number 
of  answers,  for  upon  a  given 
force,  AB,  as  diagonal  we  can 
construct  an  indefinite  number 
of  parallelograms,  a  few  of 
which  are  shown  in  Fig.  99. 
The  two  forces  into  which  a 
single  force  is  resolved  are 
called  components.  It  is  often 
convenient  to  resolve  a  force 

into  two  components  at  right  angles  to  each  other. 


FIG.  99. 


FRICTION. 

119.  Friction  a  Force ;  Coefficient  of  Friction.  Fric- 
tion is  the  force  which  opposes  the  sliding  of  one  body 
over  another. 


FRICTION.  277 

If  R  denotes  the  perpendicular  pressure  between  two 
surfaces  which  slide  over  each  other,  and  F  denotes  the 

F 

friction,  the  quotient  of  —  has  been  found  to  be  a  con- 

H 

stant  number  for  any  two  given  surfaces,  provided  the 

corresponding  surfaces  are  of  the  same  material  and  in 

the  same  condition,  and  is  called  the  coefficient  of  friction. 

The  coefficient  of  friction  is  denoted  by  the  Greek  letter 

F 

p,  that  is,  —  =  JJL,  and  consequently  F  =  pR. 
R 

Does  the  last  equation  suggest  to  you  the  propriety  of, 
calling  ft  the  "  coefficient  of  friction  "  ? 

Experiment  11O.  To  find  the  coefficient  of  friction  of 
wood  sliding  on  paper. 

Apparatus.  A  smooth  board,  about  50cm  long ;  a  block  of  wood 
such  as  you  got  the  specific  gravity  of ;  an  8-ounce  spring  balance ; 
a  sheet  of  paper  about  25cm  long  and  a  little  wider  than  the  board. 

PART  1.    Where  the  sliding  is  on  a  horizontal  plane. 

Directions.  Find  what  fraction  of  an  ounce  it  takes 
to  draw  the  pointer  down  to  the  zero  line,  when  the 
balance  is  in  a  horizontal  position.  Spread  the  paper 
smoothly  on  the  board,  fold  the  edges  of  the  paper  over 
the  sides  of  the  board,  and  fasten  by  tacks.  Lay  the  board 
horizontally.  Place  the  block  on  one  of  its  narrowest 
sides  on  the  paper.  Tie  a  thread  round  the  block,  but 
in  such  a  way  that  no  part  of  the  thread  shall  come 
between  the  block  and  the  paper.  Fasten  the  end  of  the 
thread  to  the  hook  of  the  spring  balance,  and  pull  with 
the  spring  balance  held  in  a  horizontal  position  with  a 


278  EXPERIMENTAL   PHYSICS. 

force  sufficient  to  keep  the  block  moving  with  uniform 
velocity  along  the  paper.  Record  the  force  indicated  by 
the  balance,  and  correct  this  force  for  the  error  of  the 
balance  when  held  in  the  horizontal  position. 

Then,  taking  care  as  before  that  the  thread  does  not 
lie  between  the  block  and  the  paper,  lay  the  block  on  its 
broad  side,  and  record  as  before  the  force  necessary  to 
maintain  uniform  motion. 

From  the  two  cases  just  tried,  should  you  say  that  the 
amount  of  friction  depends  upon  the  extent  of  surface  in 
contact  ? 

Now  load  the  block,  still  on  its  broad  side,  with  200g 
and  400g  in  turn,  recording  in  each  case  the  force  required 
to  maintain  uniform  motion.  Weigh  the  block  itself  in 
ounces ;  and  also  find  the  weight  in  ounces  of  the  two 
weights,  the  200g  and  the  400g.  Then  calculate  the 
coefficient  of  friction  for  each  of  the  four  cases  tried.  To 
compute  the  coefficient  of  friction,  divide  the  friction  (the 
number  of  ounces  the  spring  balance  indicated  when 
corrected  for  the  zero  error)  by  the  perpendicular  pressure 
(the  weight  of  the  block  in  ounces  plus  the  weight  in 
ounces  of  any  load  put  upon  the  block). 

What  value  do  you  get  for  the  coefficient  of  friction  ? 

PART  2.     Where  the  sliding  is  on  an  inclined  plane. 

Raise  one  end  of  the  board  until  the  unloaded  block, 
once  started,  will  slide  along  the  paper  with  uniform  veloc- 
ity. Then,  keeping  the  board  fixed  in  this  position,  meas- 
ure the  vertical  distance  from  the  under  (Why?)  side  of 
the  raised  end  to  the  table,  and  the  horizontal  distance 
from  the  foot  of  this  vertical  line  to  the  point  where  the 


FRICTION.  279 

lower  end  of  the  board  rests  upon  the  table.  The  co- 
efficient of  friction  can  be  calculated  by  dividing  the 
vertical  distance  by  the  horizontal. 

Does  the  numerical  value  which  you  get  equal  that 
which  you  got  by  the  other  method? 

NOTE.  The  angle  which  the  inclined  plane  makes  with  the  horizontal 
plane,  when  the  body  is  just  about  to  slide,  is  called  the  angle  of  repose, 
or  the  angle  of  friction. 

The  proof  of  the  statement  that  the  coefficient  of 
friction  can  be  obtained  by  dividing  the  vertical  distance 
by  the  horizontal  is  given  in  the  demonstration  of  the 
following : 

Theorem.  When  a  body  slides  with  uniform  velocity 
down  an  inclined  plane,  the  coefficient  of  friction  is  equal 
to  the  height  of  the  plane  divided  by  the  base. 

Let  0  (Fig.  100)  be  a  body  sliding  with  uniform  veloc- 
ity down  the  inclined 

0 

plane,  BA. 

T  OB 

1  o  prove  /u,  =  — —  : 


Let  OW,  OF,  and 
OR  represent  weight 
of  0,  friction,  and  per-  FIG.  100. 

pendicular  pressure  respectively. 

From  C  draw  CD  \\  OR. 

CD,  DB,  B  C  are  ||  resp.  to  OR,  OF,  OW. 

~r\~ip>         f)TP 

=  -jyp  (by  the  principle  of  the  A  of  forces). 


A  ABC  is  art.  A. 


280  EXPERIMENTAL   PHYSICS. 

CD  JL  AB  (by  the  principle  that  a  st.  line  J_  to  one  of 
two  || 's  is  _L  to  the  other). 

.  • .  A  CBD  and  AB  C  are  similar. 

CB  _  DB 
'''  AC~  CD' 

OF  _  DB 

~0*-~CD' 

OF 

And  ^  =  -—  (by  definition). 


CB 


EXAMPLES. 

1.  The  coefficient  of  friction  for  wood  on  wood  is  0.33.     How  great  a 
force  must  be  applied  to  a  block  of  wood  weighing  100  Ibs.  in  order  to 
drag  it  along  a  wooden  plank  ? 

2.  A  body  slides  with  uniform  velocity  down  a  plane  inclined  at  an 
angle  of  30°  to  the  horizon.     What  is  the  coefficient  of  friction  between 
the  body  and  the  plane  ? 

HINT.  The  hypotenuse  is  twice  the  length  of  the  side  opposite  the 
angle  of  30°. 

3.  A  body,  the  weight  of  which  is  10  Ibs.,  rests  upon  a  plane  inclined 
at  an  angle  of  30°  to  the  horizon  ;  find  the  pressure  at  right  angles  to  the 
plane,  and  the  force  of  friction  exerted. 

4.  If  the  height  of  an  inclined  plane  be  to  the  length  as  3  is  to  5,  and 
a  body  the  weight  of  which  is  15  Ibs.  be  supported  by  friction  alone,  find 
the  force  of  friction  in  pounds. 

WORK. 

12O.  Work  defined ;  Unit  of  Work.  One  important 
object  of  the  next  experiment  is  to  illustrate  and  enforce 
the  meaning  of  the  term  work  as  used  in  physics.  Work 
z's  the  overcoming  of  resistance  through  space. 


WORK.  281 

According  to  the  meaning  given  in  physics  to  the  term 
work,  the  mere  supporting  of  a  book  by  the  hand  is  not 
work;  but  if  the  book  is  raised,  work  is  done,  for  a  resist- 
ance, the  weight  of  the  book,  is  overcome  (through  a 
space). 

The  unit  of  work,  among  English-speaking  engineers,  is 
the  foot-pound  (ft.  lb.).  The  foot-pound  is  the  amount  of 
work  done  in  overcoming  the  resistance  of  a  force  of  one 
pound  through  a  distance  of  one  foot. 

If  you  should  lift  a  pound-mass  vertically  a  distance  of 
one  foot,  the  amount  of  work  done  would  be  one  foot- 
pound. 

QUESTIONS.  How  many  foot-pounds  of  work  must  be  done  in  dragging 
a  20-lb.  weight  a  distance  of  15  ft.  along  a  horizontal  plane,  if  the  coeffi- 
cient of  friction  is  0.4  ?  If  the  coefficient  of  friction  is  0.5  ? 

Experiment  111.  To  find  the  amount  of  work  done  in 
dragging  a  body  up  an  inclined  plane. 

Apparatus.  An  inclined  plane,  a  stout  plank  with  a  long  slot  cut 
through  it,  one  end  resting  on  the  floor,  the  other  end  raised  above 
the  floor,  as  shown  in  Fig.  101 ;  a  4-pound  spring  balance ;  a  small, 
strong  carriage ;  four  200s  weights,  with  which  to  load  the  carriage. 

PART  1.  To  find  the  work  done,  apart  from  that 
employed  in  overcoming  friction,  by  a  force  parallel  to 
the  incline,  in  drawing  the  loaded  carriage  (Fig.  101)  such 
a  distance  up  the  plane  as  to  make  the  vertical  rise  2  ft. 

Directions.  Along  the  incline  measure  the  distance, 
AB,  corresponding  to  a  vertical  rise  of  2  ft. ;  then  find 
the  force  parallel  to  this  incline  which  would  be  neces- 
sary to  move  the  loaded  car  with  uniform  velocity  up 
the  incline,  if  there  were  no  friction.  To  determine  and 
eliminate  the  friction  at  any  part  of  the  incline,  find  the 


282 


EXPERIMENTAL    PHYSICS. 


pull  on  the  balance  parallel  to  the  incline  required  to 
move  the  carriage  at  a  uniform  velocity  up  the  incline  at 
this  part,  and  then  the  pull  in  the  same  direction  which 
will  allow  the  carriage  to  move  with  uniform  velocity  down 


FIG.  101. 

the  incline  at  the  given  part.  The  average  of  the  two 
pulls  will  be  the  pull  that  would  be  required  if  there  were 
no  friction,  and  half  the  difference  between  the  two  forces 
will  be  the  force  required  to  overcome  the  friction  at  the 
spot  in  question.  The  diagrams  and  the  following  dis- 
cussion will,  perhaps,  make  this  clearer. 

In  the  first  diagram  (Fig.  102)  the  car  is  supposed  to 

be  moving  up  the  in- 
cline. The  friction, 
F,  and  the  resolved 
part,  #,  of  the  force 
of  gravity  oppose  the 
motion.  If  the  spring 
balance  reads  a  Ibs., 
we  have 
(1) 


FIG.  102. 


WORK. 


283 


In  the  second  diagram  (Fig.  103)  the  car  is  supposed  to 
be  moving  down  the  plane.  The  friction,  JP,  acts  in  a 
direction  opposite  to 

the    motion,   so   we  , 

have,  if  the  balance 
now  registers  b  Ibs., 
2?  =  JF+5,  or, 

=  b.     (2) 


By  adding  (1)  and  (2)  we  have,        FlG-  103- 
2x  —  a       b, 


Hence,  the  force  necessary  to  keep  the  car  moving  up  the 

incline,  if  we  leave  friction  out  of  account,  is  -      -  Ibs. 

2 

a  _  5 
By  subtracting  (2)  from  (1)  we  find,  F=  —  -  —  .      If 

2 

the  plane  were  uniform,  it  would  be  necessary  to  deter- 
mine the  force  at  one  place  only  ;  but  as  the  incline  may 
vary  slightly,  it  is  best  to  determine  the  force  at  three  or 
four  places  and  take  the  average. 

Multiply  this  average  force,  a;,  by  the  distance,  measured 
along  the  plane  through  which  the  force  would  have  to 
act  in  order  to  draw  the  car  up  the  plane  so  that  its 
vertical  rise  would  be  2  ft. 

How  many  foot-pounds  of  work  are  required? 

PART  2.  To  find  the  work,  friction  aside,  done  by  a 
force  acting  parallel  to  the  base  of  the  incline,  in  drawing 
the  loaded  car  such  a  distance  up  the  incline  as  to  make 
the  vertical  rise  2  ft. 


284  EXPERIMENTAL   PHYSICS. 

Directions.  Let  the  string  that  attaches  the  carriage 
to  the  balance  pass  through  the  slot  cut  in  the  plane,  as 
shown  in  Fig.  104.  Then  draw  the  carriage  up  the  plane, 
always  pulling  horizontally  on  the  balance.  Do  not  let 
the  string  rub  on  the  sides  of  the  slot.  By  observing  the 


pull  going  up  and  the  pull  coming  down,  eliminate  fric- 
tion, as  in  Part  1.  Measure  the  horizontal  distance,  AC, 
corresponding  to  a  vertical  rise  of  2  ft.  Multiply  the  force 
by  the  distance,  AC. 

How  many  foot-pounds  of  work  are  necessary  ? 

PART  3.  To  find  the  amount  of  work  done  in  raising 
the  carriage  and  contents  through  a  vertical  distance  of 
2ft. 

Directions.  Weigh  the  carriage  and  its  load  together 
on  the  same  balance. 

How  many  foot-pounds  of  work  would  it  take  to  raise 
the  carriage  and  its  load  through  a  vertical  distance  of 
2ft.? 

How  do  the  amounts  of  work  in  the  three  cases  compare 
with  each  other? 


WORK.  285 

121.  Law  of  the  Inclined  Plane.  The  teachings  of 
the  preceding  experiment  lead  to  a  very  important  result, 
known  as  the  law  of  the  inclined  plane. 

The  amount  of  work  done  in  dragging  a  body  up  an 
inclined  plane  is  equal  to  the  weight,  W,  of  the  body  mul- 
tiplied by  the  height,  OB,  of  the  plane  (Fig.  105),  whether 
the  force  used  to  drag  the  body  acts  parallel  to  the  in- 
cline, AB,  or  parallel  to  the 
base,  AC,  consequently,  if 
P  denotes  the  force  par- 
allel to  AB  necessary  to 
drag  the  body,  and  Q  the 
force  parallel  to  AC, 

P  x  AB  =  W  X  CB,      " 

QXAO=WXCB, 

that  is,  the  force  required  to  draff  the  body  multiplied  by  the 
distance  through  which  it  acts  is  equal  to  the  weight  of  the 
body  multiplied  by  the  vertical  distance  through  which  it  is 
raised. 

EXAMPLES. 

1.  A  body  weighing  100  Ibs.  rests  upon  an  incline,  (a)  How  much 
work  must  be  done  in  drawing  the  body  10  ft.  up  this  incline,  the  vertical 
ascent  being  6  ft.  ? 

Solution.     100  X  6  =  600  ft.  Ibs. 

(6)  What  force  is  necessary  to  draw  the  body  up  the  incline,  if  applied 
parallel  to  the  incline  ? 

Solution.     P  X  10  =  100  X  6 ;  hence,  P  =  60  Ibs. 

(c)  What  force  is  necessary  to  draw  the  body  up  the  incline  if  applied 
parallel  to  the  base  ? 

Solution.     Q  x  V~102  -  62  =  100  X  6 ;  hence  SQ  =  600,  .-.  Q  =  75  Ibs. 

(d)  How  much  work  must  be  done  if  the  coefficient  of  friction  is  0.2  ? 
Solution.     100  X  6  +  80  X  0.2  X  10  =  760  ft.  Ibs. 


286  EXPERIMENTAL    PHYSICS. 

NOTE.  In  the  solution  of  (d),  the  expression  80  X  0.2  X  10  is  obtained 
by  applying  the  principle  of  the  triangle  of  forces. 

2.  A  block  weighing  10  Ibs.  rests  on  an  incline  such  that  the  block 
must  move  5  ft.  in  order  to  rise  3  ft.     The  pressure  of  the  block  against 
the  incline  is  in  this  case  8  Ibs.     The  coefficient  of  friction  is  0.25.     How 
much  work  must  be  done  against  gravity  by  a  force  parallel  to  the  incline 
in  drawing  the  block  up  5  ft.     How  much  work  against  friction  ? 

3.  An  inclined  plane  rises  3.5  ft.  for  every  5  ft.  of  length.     Find  what 
force  in  pounds  must  be  applied  parallel  to  the  incline  to  drag  up  a 
weight  of  200  Ibs. 

4.  A  railway  train  weighing  30  tons  is  drawn  up  an  inclined  plane  of 
1  ft.  in  60  by  means  of  a  rope  and  a  stationary  engine  ;  find  what  num- 
ber of  pounds  at  least  the  rope  should  be  able  to  support. 

5.  If  the  base  of  an  inclined  plane  is  to  the  height  as  24  is  to  7,  find 
the  force  necessary  to  drag  a  body  weighing  48  Ibs.  up  the  plane. 

(a)    When  the  force  acts  parallel  to  the  incline. 
(&)    When  the  force  acts  parallel  to  the  base. 

6.  While  a  car  moves  along  a  track  a  distance  of  10  ft. ,  a  man  pushes 
with  a  force  of  25  Ibs.  against  the  side  of  the  car  in  a  direction  at  right 
angles  to  the  track.     Does  the  push  of  the  man  on  the  car  assist  its 
motion?     Does  his  push,  except  by  possibly  increasing  the  friction, 
retard  the  motion  of  the  car  ?     How  many  foot-pounds  of  work  does  the 
man  do  upon  the  car  during  its  motion  ? 

INERTIA. 

122.  Inertia  a  Property  of  Matter.  There  is  an 
inherent  property  of  matter  called  inertia,  which  makes 
the  application  of  a  force  necessary  to  bring  about  any 
change  in  the  direction  or  magnitude  of  a  body's  motion. 

To  start  a  body  requires  the  application  of  force;  to 
stop  a  body  requires  the  application  of  force ;  to  deflect 
a  moving  body  from  its  path  also  requires  the  application 
of  force. 

In  brief,  to  start  a  body,  to  stop  it,  to  increase  its  veloc- 
ity, to  diminish  its  velocity,  or  to  deflect  it  from  its  path, 


INERTIA.  287 

the  application  of  a  force  is  required.  The  property  of 
matter  that  makes  this  application  of  force  necessary  is 
called  inertia. 

To  get  the  quantity  of  matter  in  a  body,  we  have  com- 
pared the  body,  by  means  of  a  pan  balance,  with  a  stand- 
ard mass.  Since  the  attraction  of  the  earth  becomes  greater 
as  we  approach  the  polar  regions  from  the  equatorial,  a 
mass  of  matter  would  weigh  more  at  the  pole  than  at  the 
equator.  The  spring  balance  does  not  measure  the  mass, 
that  is,  the  quantity  of  matter  a  body  contains,  but  it  does 
measure  the  force  of  gravity  at  different  parts  of  the 
earth's  surface. 

123.    Definition  of  the  Equality  of  Two  Masses.     In 

our  discussion  of  the  term  mass  in  the  early  part  of  this 
chapter  we  tacitly  assumed  that  two  bodies  have  the  same 
mass,  no  matter  how  much  they  may  differ  in  substance, 
provided  they  are  in  equilibrium  when  placed  in  the 
opposite  pans  of  a  balance. 

The  idea  of  inertia,  however,  gives  us  a  means  of  com- 
paring two  masses  for  equality  without  the  use  of  a 
balance  of  any  description.  The  method  holds  not  only 
for  the  earth,  but  for  all  the  heavenly  bodies  also,  as  well 
as  for  all  regions  of  space.  In  the  following  experiment 
we  shall  apply  this  "inertia  test"  for  the  equality  of  two 
masses. 

Experiment  112.  To  find,  without  the  use  of  a  balance, 
whether  two  masses  are  equal  or  not. 

Apparatus.  The  mass-tester  (Fig.  106),  consisting  of  a  vertical 
axis  with  two  horizontal  arms  to  carry  cups  (nickel-plated  calorime- 
ters), and  a  spiral  spring  with  one  end  fastened  to  the  axis  and 


288 


EXPERIMENTAL   PHYSICS. 


the  other  fastened  to  the  support  in  which  the  upper  end  of  the  axis 
is  pivoted ;  two  100s  weights ;  some  lead  shot ;  a  platform  balance. 

Directions.  In  each  of  the  cups  put  a  100g  mass,  turn 
the  axis  through  180°,  and  find  accurately  the  time  of 
six  vibrations.  Then  take  out  the  100g  mass  and  put  in 
place  of  it  lead  shot ;  try  to  have  equal 
amounts  of  shot  in  each  of  the  cups  so 
that  the  axis  shall  not  bind  where  it  is 
pivoted.  By  varying  the  amount  of  shot 
(adding  more  if  the  apparatus  moves  too 
fast,  taking  out  some  if  the  apparatus 
moves  too  slowly),  get  the  apparatus  to 
make  the  same  number  of  vibrations  in 
the  same  time  as  when  the  iron  occupied 
the  place  of  the  lead.  Find  how  many 
grams  the  shot  weighs. 

VELOCITY. 


FIG.  106. 


124.  Measure  of  the  Velocity  of  a 
Body.  Whenever  a  body  moves  (that 
is,  changes  its  position)  it  either  passes 
over  equal  spaces  in  equal  times,  like  the  hand  of  a  clock, 
and  is  said  to  have  constant  velocity,  or  else  passes  over 
unequal  spaces  in  equal  times,  like  a  stone  falling  from 
a  height  toward  the  ground.  From  the  instant  the  stone 
begins  its  downward  motion,  it  falls  with  greater  and 
greater  swiftness  until  it  rests  upon  the  ground.  When 
the  body  passes  over  unequal  spaces  in  equal  times,  its 
velocity  is  said  to  be  variable. 

^Definition,     Velocity  is  the  rate  of  motion  of  a  body. 


ACCELERATION.  289 

The  velocity  of  a  body  is  measured  by  the  distance 
traversed  divided  by  the  time  that  elapses  during  the 
journey. 

If  we  denote  by  s  the  distance  traversed  in  time,  t,  by 
a  body  moving  with  constant  velocity,  v,  we  have 


EXAMPLES. 

1.  If  the  tip  of  a  clock-hand  moves  a  distance  of  30cm  in  20  minutes, 
what  is  the  velocity  ? 

Solution.     We  are  to  find  the  number  of  units  of  length  traversed  in 
a  unit  of  time.     If  we  take  as  our  unit  of  length  the  centimeter,  and  as 

30 

our  unit  of  time  the  minute,  the  required  velocity  will  be  —  =  1.5cm  per 

zo 

minute. 

If  we  take  as  our  unit  of  length  the  centimeter,  as  before,  and  for  our  unit 

30  1 

of  time  the  second,  the  required  velocity  will  be  =  —  =  0.026cm 

^U  X  ou        4U 

per  second. 

O  1 

2.  Is  a  velocity  of  -cm  per  minute  the  same  as  a  velocity  of  — cra  per 
second  ? 

3.  If  a  tortoise  walk  at  the  rate  of  3  in.  a  second,  how  many  feet  will 
he  go  in  an  hour  ? 

4.  How  many  seconds  would  a  train  take  to  go  0.2  of  a  mile  at  the 
rate  of  20  miles  per  hour  ? 

5.  With  what  velocity  must  a  horse  trot  in  order  to  .go  780  yds.  in 
1  minute  ? 


ACCELERATION. 

125.  Measure  of  Acceleration.  When  a  body  is  mov- 
ing with  a  variable  velocity,  the  rate  at  which  the  velocity 
changes  is  called  acceleration.  It  is  measured  by  the 


290  EXPERIMENTAL   PHYSICS. 

velocity  gained  by  the  body  in  a  certain  time,  divided  by 
the  time  taken  to  gain  it. 

Acceleration  is  said  to  be  constant  when  the  velocity 
gains  equal  additions  of  acceleration  in  equal  times. 

Variable  acceleration,  which  we  shall  have  no  occa- 
sion to  consider,  results  when  the  velocity  gains  unequal 
additions  of  acceleration  in  equal  times. 

For  each  second  the  acceleration  of  a  body  falling  in 
a  vacuum  near  the  surface  of  the  earth  is  constant,  and 
is  equal  to  about  980cm  per  second. 

If  a  body  moving  with  a  velocity  which  has  a  constant 
acceleration,  «,  has  a  velocity  of  VQ  at  the  beginning  of  the 
time,  £,  and  a  velocity  of  v±  at  the  end  of  this  time,  we 
have  _  _  „ 

(2) 


EXAMPLES. 

1.  If  the  velocity  of  a  falling  body  after  3  seconds  is  2840cm  per  second, 
what  is  its  acceleration  ? 

Solution.  We  are  to  find  the  number  of  units  of  velocity  acquired  in 
a  unit  of  time.  If  we  take  as  our  unit  of  velocity  the  centimeter  per 
second,  the  acceleration  in  1  second  will  be 

2840 

— —  =  980cm  per  second, 
o 

2.  If  a  body  is  thrown  downward  with  an  initial  velocity  of  100cm  per 
second  from  a  balloon,  and  after  the  lapse  of  3  seconds  its  velocity  is 
2940cm  per  second,  what  is  its  acceleration  ? 

Solution.  As  acceleration  is  the  gain  in  velocity  divided  by  the  time 
taken,  in  this  case  3  seconds,  in  making  this  gain  we  have  for  the  accelera- 
tion in  1  second 

2940  - 100      2840      non 

— =  — —  =  980cm  per  second. 

3  o 

3.  A  body  starts  from  rest  and  acquires  a  velocity  of  1200cm  per  second 
in  half  a  minute  ;  what  is  its  acceleration  ? 


-DISTANCE   TRAVERSED.  291 

4.  A  body  starts  with  a  velocity  of  75cm  per  second,  and  5  seconds 
afterward  is  moving  with  a  velocity  of  97cm  per  second;   what  is  its 
acceleration  in  1  second  ? 

5.  Starting  with  a  velocity  of  25cm  per  second,  a  body  for  every  sec- 
ond it  moves  has  an  acceleration  of  980cm  per  second ;  what  will  be  its 
velocity  in  1,  2,  3,  and  6  seconds,  respectively  ? 


DISTANCE   TRAVERSED. 

126.    Distance  traversed  by  a  Moving  Body.     If  the 

initial  velocity  of  a  moving  body  is  v0,  and  the  velocity  it 
has  at  the  end  of  the  time,  £,  is  vv  its  average  increase  of 
velocity  will  be 


2 

and  denoting  by  s  the  distance  passed  over  by  the  body 
by  reason  of  the  increase  of  velocity  from  VQ  to  vv  we  have 

(3) 
But  v  l  —  VQ  =  at  by  (2), 


EXAMPLES. 

1.   How  far  will  a  body  fall  in  2  seconds  ? 

Solution.  The  relation  existing  between  the  time  during  which  a 
body  moves,  under  a  constant  acceleration,  and  the  distance  traversed 
by  the  body  in  this  time  is 


2.   How  much  farther  will  a  body  fall  during  the  second  second  of  its 
fall  than  during  the  first  ? 


292  EXPERIMENTAL   PHYSICS. 


980  X  2^ 
Solution.     The  distance  fallen  in  2  seconds  =  -  -  -  =  1960cm. 

„      ,.,       „       =  980  XI'  =490cm 

Hence,  the  distance  traversed  during  the  second  second  will  be 
1960cm  _  4900™  =  1470cm. 

3.    Show  that  the  distance  passed  over  in  the  (t  +  1)  second  by  a  body 
acted  upon  by  a  constant  acceleration,  a,  is  f  (2t  +  1). 

cifi 
Solution.     Distance  traversed  in       t       seconds  =  —  . 


Hence,  the  distance  traversed  in  the  (t  +  1)  second  is 


4.  Show  that  the  distance  passed  over  during  the  2  seconds  immediately 
following  the  Zth  second  by  a  body  starting  from  rest  and  moving  under 
a  constant  acceleration,  a,  is  2a  (t  +  1). 

5.  How  many  seconds  will  a  falling  body,  starting  from  rest,  require 
to  fall  490'm  ? 

6.  Two  bodies  are  let  fall  from  the  same  point  at  an  interval  of 
2  seconds  ;  find  how  many  centimeters  they  will  be  apart  at  the  end  of  6 
seconds  from  the  fall  of  the  first,  the  acceleration  of  gravity  being  981cm 
per  second. 

QUANTITY    OF   MOTION. 

127.  Momentum.  If  two  bodies,  one  having  twice 
the  mass  of  the  other,  are  moving  with  equal  velocity,  the 
greater  mass  has  the  greater  quantity  of  motion.  If  the 
bodies  of  equal  mass  are  moving  with  unequal  velocities, 
the  body  moving  with  the  greater  velocity  has  the  greater 
quantity  of  motion.  The  quantity  of  motion,  then,  which 
a  body  has,  depends  upon  the  mass  of  the  body  and  upon 
the  velocity  with  which  it  is  moving  ;  so  we  define  the 


QUANTITY    OF    MOTION.  293 

momentum  (which  means,  simply,  quantity  of  motion)  of 
a  body  as  the  product  of  the  mass  of  the  body  and  its 
velocity.  If  the  mass  of  a  body  is  m  and  its  velocity  v, 
its  momentum  is  mv. 

The  meaning  of  momentum  will  be  illustrated  by  the 
next  experiment,  which  has  for  its  object  the  comparison 
of  the  total  amount  of  momentum  of  two  masses  before 
colliding  with  each  other,  and  the  total  amount  of  momen- 
tum of  the  two  masses  after  collision. 

Experiment  113.  To  find  how  the  total  amount  of 
momentum  of  two  masses  before  collision  compares  with  the 
total  amount  of  momentum  after  collision. 

Apparatus.  Two  ivory  balls,  one  weighing  about  50s,  the  other 
about  200« ;  a  flat  bar  of  wood  about  50cm  long,  and  of  a  width 
somewhat  greater  than  the  sum  of  the  radii  of  the  balls ;  a  piece  of 
apparatus  like  that  shown  in  Fig.  107 ;  fine  iron  wire,  No.  33  B.  &  S. 

PART  1.  When  the  larger  ball  strikes  the  smaller  at 
rest. 

Directions.  Fasten  the  flat  bar,  in  a  horizontal  position, 
as  high  above  the  floor  as  practicable.  Into  each  end  of 
the  bar  drive  two  tacks,  whose  distance  apart  shall  equal 
the  sum  of  the  radii  of  the  balls.  To  one  of  these  tacks 
fasten  one  end  of  a  long  piece  of  fine  iron  wire,  pass  the 
other  end  through  a  little  screw-eye  in  one  of  the  ivory 
balls.  Then  carry  this  end  to  the  tack  driven  into  the 
other  end  of  the  board  directly  opposite  the  first,  and 
there  fasten  the  wire,  after  drawing  it  up  till  the  ball, 
when  hanging  freely,  almost  touches  the  center  of  the 
scale,  which  is  shown  in  Fig.  107.  The  other  ball  should 


294  EXPERIMENTAL   PHYSICS. 

be  suspended  in  the  same  way.  The  positions  of  the 
balls  should  then  be  adjusted  till  their  centers  are  in  a 
horizontal  line,  and  directly  over  the  scale.  Record  the 
weight  of  each  ball,  and  also  the  weight  of  the  wire  which 
supports  each. 

Allowing  the  smaller  ball  to  hang  at  rest,  draw  the 
larger  ball  through  an  arc  of  about  10°,  keeping  it  over 


FIG.  107. 

the  scale.  Record  the  reading  on  the  scale  directly 
beneath  each  ball.  Then  release  the  larger  ball,  and 
again  observe  and  record  the  readings,  when  the  balls 
have  swung  as  far  as  they  will  after  collision. 

Through  how  many  centimeters,  as  measured  on  the 
scale,  did  the  larger  ball  move  before  collision  ? 

Through  how  many  centimeters  did  the  larger  ball 
move  after  collision  ? 

Through  how  many  centimeters  did  the  smaller  ball 
move  after  collision? 

Make  this  trial  several  times,  always  drawing  the  larger 
ball  through  the  same  arc,  and  take  the  average  of  the 
corresponding  readings  in  the  several  trials. 

When  experimenting  with  the  simple  pendulum,  you 
found  that  the  length  of  the  arc  through  which  the  pen- 
dulum swung  made  no  perceptible  difference  in  the  time 


QUANTITY    OF    MOTION.  295 

of  an  oscillation.  In  the  present  case,  the  velocity  with 
which  the  larger  ball  is  moving,  when  it  hits  the  smaller, 
is  proportional  to  the  distance  through  which  it  has 
moved ;  also  the  velocity  with  which  the  smaller  ball  starts 
after  it  has  been  hit  by  the  larger  is  proportional  to  the 
distance  it  moves  until  it  starts  to  swing  back ;  and  the 
distance  the  larger  ball  moves  after  the  collision  is  pro- 
portional to  the  velocity  which  it  had  just  after  the  colli- 
sion. As  we  wish  only  to  compare  the  momenta  of  the 
balls  before  impact  with  the  momenta  after  impact,  we 
shall  use  these  distances  in  place  of  the  actual  velocities 
to  which  they  are  proportional. 

The  following  questions  will  show  the  line  of  reasoning 
by  which  the  result  is  reached : 

(1)  What  is   the   product  of  the   mass   of   the  larger 
ball  plus  half  the  mass  of  its  supporting  wire,  and  the 
distance    through    which   it   moved   before    striking   the 
smaller  ? 

(2)  Calling   the  product,  asked  for  in   the   preceding 
question,  momentum,   what   was    the    momentum    of   the 
smaller  ball  before  it  was  struck  by  the  larger  ? 

(3)  What  was  the  momentum  of  the  larger  ball  after 
collision  ? 

(4)  What  was  the  momentum  of  the  smaller  ball  after 
collision  ? 

(5)  How  does  the  sum  of  the  answer  to  (1)  and  the 
answer  to  (2)  compare  with  the  sum  of  the  answer  to  (3) 
and  the  answer  to  (4)  ? 

Why  was  only  half  of  the  weight  of  the  suspending 
wire  added  in  each  case  to  the  weight  of  the  ball  ? 


296  EXPERIMENTAL   PHYSICS. 

PART  2.    When  the  smaller  ball  strikes  the  larger  at  rest. 

Directions.  The  apparatus  should  be  arranged  as  for 
Fart  1. 

Proceed  as  in  Part  1,  but  allow  the  larger  ball  to  hang 
at  rest,  and  draw  the  smaller  one  through  an  arc  of  about 
10°  and  then  release  it.  As  before,  repeat  the  trial  and 
record  the  readings. 

Through  how  many  centimeters  did  the  smaller  ball 
move  before  collision? 

Through  how  many  centimeters  did  the  smaller  ball 
move  after  collision  ? 

Through  how  many  centimeters  did  the  larger  ball 
move  after  collision? 

(1)  What   was    the    momentum    of   the    smaller  mass 
before  collision  ? 

(2)  What  was  the  momentum  of  the  larger  mass  before 
collision  ? 

(3)  What  was  the  momentum  of  the  smaller  mass  after 
collision  ? 

(4)  What  was  the  momentum  of  the  larger  mass  after 
collision  ? 

(5)  How  does  the  sum  of  the  answer  to  (1)  and  the 
answer  to  (2)  compare  with  the  sum  of  the  answer  to  (3) 
and  the  answer  to  (4)  ? 

NOTE.  When  a  ball,  as  the  smaller  one  in  this  case,  moves  after 
collision  in  the  opposite  direction  to  that  in  which  It  was  moving  before 
collision,  its  velocity  is  negative,  and  therefore  its  momentum  is  also 
negative  ;  so  when  we  get  the  sum  of  the  answers  to  (3)  and  (4),  it  is  the 
algebraic  sum  which  is  required. 

PART  3.  When  the  balls,  moving  from  opposite  direc- 
tions, meet  at  their  point  of  rest. 


QUANTITY   OF    MOTION.  297 

Directions.  Draw  each  of  the  balls  through  an  arc  of 
about  10°  and  release  them,  taking  and  recording  as 
before  the  readings  of  their  various  positions. 

Through  how  many  centimeters  did  the  larger  ball 
move  before  collision  ? 

Through  how  many  centimeters  did  the  smaller  ball 
move  before  collision  ? 

Through  how  many  centimeters  did  the  smaller  ball 
move  after  collision  ? 

Through  how  many  centimeters  did  the  larger  ball 
move  after  collision  ? 

Remembering  that,  if  velocity  in  one  direction  is  con- 
sidered positive,  velocity  in  the  opposite  direction  is  nega- 
tive, find  the  algebraic  sum  of  the  momenta  of  the  two 
masses  before  collision;  also  the  algebraic  sum  of  the 
momenta  of  the  two  masses  after  collision. 

How  does  the  first  sum  compare  with  the  second  ? 

EXAMPLES. 

1.  A  ball  weighing  20s  moving  north  with  a  velocity  of  50cm  per  sec. 
strikes  centrally  a  ball  weighing  100s  which  is  at  rest.  After  the  collision 
the  larger  ball  moves  north  with  a  velocity  of  12cm  per  sec.  What  velocity 
has  the  smaller  ball  after  the  collision,  and  in  what  direction  is  it  moving  ? 
Solution.  Let  x  denote  the  velocity  of  the  smaller  ball  after  the  colli- 
sion. We  have 

100  X    0  =       0  momentum  of  larger  ball  before  collision. 
20  X  50  =  1000  "  "  smaller  "         "  " 

100  X  12  =  1200  "  "  larger     "     after        " 

20x-x=  20x  "  "smaller  "         "  " 

But  the  total  momentum  before  collision  is  equal  to  the  total  momentum 
after  collision ;  hence 

0+  1000=  1200  +  20  x 


298  EXPERIMENTAL    PHY-S1CS. 

That  is,  the  smaller  ball  is  moving  after  the  collision  with  a  velocity  of 
10cm  per  sec.  towards  the  south.  The  minus  sign  denotes  that  the  direc- 
tion of  motion  is  opposite  that  which  the  ball  had  before  the  collision. 

2.  If  a  ball  of  mass  25s  moving  with  a  velocity  of  60cm  per  sec.  strikes 
centrally  another  ball  at  rest  the  mass  of  which  is  100?,  and  then  rebounds 
with  a  velocity  of  20cm  per  sec.,  with  what  velocity  does  the  larger  ball 
move  after  the  collision  ? 

3.  A  ball  of  mass  200s  moving  with  a  velocity  of  30cm  per  sec.  strikes 
centrally  another  ball  of  mass  65s  at  rest.     After  the  collision  the  larger 
ball  moves  on  with  a  velocity  of  17cm  per  sec.     With  what  velocity  does 
the  smaller  ball  move  after  the  collision  ? 

4.  A  ball  of  mass  75s  moving  north  with  a  velocity  of  200cm  per  sec. 
strikes  centrally  another  ball  of  mass  60s  moving  south  with  a  velocity  of 
100cm  per  sec.    After  the  collision  the  larger  ball  moves  on  with  a  velocity 
of  30cm  per  sec.  What  is  the  velocity  of  the  smaller  ball  after  the  collision, 
and  in  what  direction  is  it  moving  ? 

ABSOLUTE   UNIT    OP   FORCE. 

128.  The  Dyne.  The  units  of  force  which  we  have 
used  in  our  work  in  the  laboratory  have  been  gravitational 
units,  or  units  of  force  depending  for  their  value  upon  the 
pull  of  gravity.  As  the  force  of  gravity  is  not  constant, 
but  increases  in  strength  as  we  go  from  the  equator 
towards  either  pole,  a  unit  of  force  has  been  adopted 
called  the  dyne,  which  is  independent  of  the  earth's 
attraction,  and  remains  constant  for  all  parts  of  the  uni- 
verse. The  dyne  is  a  unit  of  force  which  depends  upon 
the  inertia  of  matter.  (See  definition  of  inertia,  page  286.) 

Definition.  The  dyne  is  that  force  which,  acting  upon  a 
mass  of  I9  for  one  second,  gives  it  a  velocity  of  lcm  per  second. 

If  the  dyne  acts  for  2  sec.  on  a  mass  of  lg,  the  velocity 
imparted  will  be  2cm  per  sec. ;  for  3  sec.,  3cm  per  sec.;  and 
so  on. 


ABSOLUTE    UNIT    OF    WOIiK.  299 

If  a  force  of  2  dynes  acts  for  1  sec.  on  a  mass  of  lg,  the 
velocity  imparted  will  be  2cm  per  sec. ;  for  3  dynes,  3cm 
per  sec. 

If  the  dyne  acts  on  a  mass  of  2g  for  1  sec.,  the  velocity 
imparted  will  be  J-cm  per  sec. ;  on  a  mass  of  3g,  ^cm  per  sec. 

If  /  denotes  the  number  of  dynes,  m  the  number  of 
grams  acted  upon,  t  the  number  of  seconds  the  action 
lasts,  and  v  the  velocity  acquired, 

,=i        (4) 

m 
Equation  (4)  on  clearing  it  of  fractions  takes  the  form 

mv  =  ft. 

This  equation  expressed  in  words  is :  "  The  momentum 
of  a  body  is  equal  to  the  force  acting  upon  it  multiplied 
by  the  time  the  force  has  been  acting." 

ABSOLUTE   UNIT    OF  WORK. 

129.  The  Erg1.  Work  has  already  been  defined  as 
the  overcoming  of  resistance ;  and  work  is  measured  by 
the  product  of  the  force  (used  in  overcoming  the  resist- 
ance) and  the  distance  through  which  the  force  acts. 

If  the  dyne  be  taken  as  the  unit  of  force  and  the  centi- 
meter as  the  unit  of  distance,  then  the  unit  of  work  is  the 
work  done  by  one  dyne  acting  through  a  distance  of  lcm. 
This  unit  of  work  is  called  the  erg  (from  the  Greek  ergon, 
work).  The  erg  is  an  absolute  unit  of  work,  while  the 
foot-pound  is  a  gravitational  unit  of  work.  The  erg  is  a 
unit,  the  magnitude  of  which  remains  unchanged  in  what- 
ever part  of  the  universe  it  may  be  employed ;  while  the 
foot-pound  could  be  used  nowhere  except  upon  the  surface 


300  EXPERIMENTAL   PHYSICS. 

of  the  earth,  and  even  then  it  would  have  different  values 
at  different  parts  of  the  earth's  surface. 

SYSTEMS    OF   UNITS. 

13O.  The  English  System;  the  Ceiitimeter-gram- 
second  System.  In  the  English  System  the  foot  is 
taken  as  the  unit  of  length,  the  pound  as  the  unit  of 
mass,  and  the  second  as  the  unit  of  time,  while  in  the 
Centimeter-gram-second  System  (often  written  in  the  ab- 
breviated form  C.G.S.  System),  the  centimeter  is  taken  as 
the  unit  of  length,  the  gram  as  the  unit  of  mass,  and  the 
second  as  the  unit  of  time. 

The  following  list  of  units  with  their  definitions  is 
important : 

UNITS  OF  FORCE. 

ENGLISH  SYSTEM.  C.G.S.  SYSTEM. 

Gravitation,  Pound,  Gram. 

Absolute,  Poundal,  Dyne. 

UNITS  or  WORK. 

ENGLISH  SYSTEM.  C.G.S.   SYSTEM. 

Gravitation,  Foot-pound,  Gram-centimeter. 

Absolute,  Foot-poundal,  Erg. 

The  gravitation  unit  of  force,  the  pound,  is  the  pull  of 
the  earth  upon  a  mass  of  one  pound. 

The  absolute  unit  of  force,  the  poundal,  is  that  force 
which,  acting  upon  the  pound-mass  for  one  second,  will 
give  it  a  velocity  of  one  foot  per  second. 

The  gravitation  unit  of  work,  the  foot-pound,  is  the 
amount  of  work  done  in  lifting  the  pound-mass  one  foot 
high  in  opposition  to  the  force  of  gravity ;  or,  what  is  the 


SYSTEMS   OF    UNITS.  301 

same  thing,  the  foot-pound  is  the  amount  of  work  done  in 
overcoming  the  force  of  one  pound  through  a  distance  of 
one  foot. 

The  absolute  unit  of  work,  the  foot-poundal,  is  the 
amount  of  work  done  in  overcoming  a  resistance  of  one 
poundal  through  a  distance  of  one  foot. 

The  gravitation  unit  of  force,  the  gram,  is  the  pull  of 
the  earth  upon  a  mass  of  one  gram. 

The  absolute  unit  of  force,  the  dyne,  is  that  force 
which,  acting  upon  the  gram-mass  for  one  second,  will 
give  it  a  velocity  of  one  centimeter  per  second. 

The  gravitation  unit  of  work,  the  gram-centimeter,  is 
the  amount  of  work  done  in  lifting  the  gram-mass  one 
centimeter  high  in  opposition  to  the  force  of  gravity  ;  or, 
what  is  the  same  thing,  the  gram-centimeter  is  the  amount 
of  work  done  in  overcoming  the  force  of  one  gram  through 
a  distance  of  one  centimeter. 

The  absolute  unit  of  work,  the  erg,  is  the  amount  of 
work  done  in  overcoming  a  resistance  of  one  dyne  through 
a  distance  of  one  centimeter. 

131.  Energy.  Energy  is  the  ability  of  doing  work, 
and  is  measured  by  the  work  done. 

Thus,  if  a  force  of  /  dynes  is  overcome  through  a  dis- 
tance of  scm,  the  work  done  =  fs  ergs,  fs  is  also  the 
measure  of  the  energy  expended. 

-^  ,.      mv 

From  (4)  /  =  —  . 


But  *  = 


mv      1  mvat 


302  EXPERIMENTAL    THYSICS. 

But  at  =  v. 

(5) 

997?) 

The  quantity  -— -  is  denoted   by  the  expression  "the 

Z 

kinetic  energy  of  the  body."  So  we  may  say  that  the 
kinetic  energy  of  a  body  is  found  by  multiplying  the 
mass  of  the  body  by  the  square  of  the  velocity,  and  taking 
half  the  product. 

132.  Conservation  of  Energy.  A  body  raised  above 
the  surface  of  the  earth  has  potential  energy,  or  energy  of 
position ;  but  when  the  body  falls,  it  will  perform  just  as 
much  work  as  was  necessary  to  raise  it.  In  the  act  of 
falling,  the  body's  potential  energy  will  be  changed  into 
kinetic  energy,  or  energy  of  motion ;  consequently  what 
the  body  loses  in  potential  energy,  it  gains  in  kinetic. 
On  the  instant  of  striking  the  ground,  all  the  body's 
potential  energy  has  been  changed  into  kinetic  energy. 

When  the  body  was  falling,  the  total  amount  of  energy 
it  possessed,  considering  both  potential  and  kinetic,  was 
no  more,  no  less,  but  always  the  same.  It  is  true  that  the 
form  of  the  energy  was  always  changing,  a  greater  and 
greater  quantity  becoming  kinetic  at  the  expense  of  the 
potential ;  the  sum  total,  however,  of  all  the  energy  pos- 
sessed by  the  body  remained  constant.  This  doctrine  of 
the  preservation  or  indestructibility  of  energy,  usually 
called  the  conservation  of  energy,  is  of  the  greatest  impor- 
tance in  physics.  Just  as  water  may  exist  in  any  one 
of  the  forms,  solid,  liquid,  or  gaseous,  and  yet  remain 
water,  just  so  may  energy  exist  in  various  forms  and  still 


THERMODYNAMICS.  303 

remain  energy.  Heat,  light,  and  sound  are  forms  of 
energy.  When  the  falling  body,  about  which  we  have 
been  speaking,  strikes  the  ground,  there  is  a  change  of 
form  of  its  kinetic  energy:  a  part  appears  as  heat,  causing 
an  increase  in  the  temperature  of  the  body ;  another  part 
produces  vibrations  of  the  air,  which  reach  the  ear  as 
sound,  and  if  the  body  is  of  sufficient  hardness,  a  flash  of 
light  may  be  seen.  The  body  may,  too,  throw  up  a  little 
earth  when  it  strikes  the  ground,  and  also  produce  tremors 
and  vibrations  in  the  ground  where  it  falls,  so  the  kinetic 
energy  which  the  body  had  in  striking  the  ground  has 
been  changed  from  the  kinetic  form  into  that  of  heat, 
sound,  etc.;  but  the  sum  of  the  amounts  of  energy  in  each 
of  the  separate  forms  is  equal  to  that  in  the  kinetic  form. 
Though  its  form  may  change,  energy  itself  is  indestruc- 
tible ;  its  amount  in  the  universe  is  always  the  same. 

THERMODYNAMICS. 

133.  Mechanical  Equivalent  of  Heat.  Whenever 
one  body  is  rubbed  by  ariother,  heat  results ;  also  whenever 
a  piece  of  metal  is  hammered,  the  metal  grows  hot.  In 
each  of  these  cases  mechanical  action  has  been  expended, 
and  heat  has  been  a  result.  In  brief,  then,  heat  has  been 
a  result  of  work.  We  have  already  become  acquainted 
with  a  unit,  the  calorie,  with  which  to  measure  quantities 
of  heat,  and  also  with  the  gram-centimeter,  with  which  to 
measure  work.  It  will  be  the  object  of  the  present  article 
to  give  a  concise  account  of  the  method  of  finding  the 
relation  between  the  unit  of  heat  and  the  unit  of  work ;  in 
other  words,  of  finding  how  many  gram-centimeters  are 
equivalent  to  one  calorie. 


304  EXPERIMENTAL    PHYSICS. 

The  first  precise  numerical  determination  of  this  rela- 
tion was  made  by  Joule,  in  the  following  manner : 

An  upright  cylindrical  vessel  is  filled  with  water  of  a 
known  temperature.  A  vertical  shaft  stands  in  the  vessel. 
Extending  from  the  sides  of  this  shaft,  in  a  horizontal 
direction,  are  paddles,  which,  when  the  shaft  is  turned, 
pass  between  stationary  vanes  projecting  from  the  sides  of 
the  vessel.  The  paddles  and  the  vanes  keep  the  water 
thoroughly  stirred  when  the  shaft  is  turned.  By  means 
of  an  arrangement  of  wheels  and  a  flexible  string,  the 
shaft  is  kept  turning  by  a  heavy  body  of  known  weight 
attached  to  the  end  of  the  string,  and  allowed  to  descend 
like  a  clock-weight. 

As  time  goes  on,  and  the  water  continues  to  be  stirred, 
the  temperature  of  the  water  rises.  At  the  end  of  the 
experiment,  the  number  of  degrees  through  which  the 
temperature  of  the  water  has  risen  is  noted;  also  the 
distance  through  which  the  heavy  body  has  fallen.  After 
making  necessary  corrections  for  friction,  the  weight  of 
the  heavy  body  multiplied  by  the  distance  through  which 
it  has  descended  gives  the  amount  of  work  expended  in 
raising  the  temperature  of  the  water.  After  making  neces- 
sary corrections  for  the  loss  of  heat  from  the  water,  the 
weight  of  the  water  multiplied  by  the  number  of  degrees 
through  which  its  temperature  has  been  raised  gives  the  num- 
ber of  units  of  heat  received  by  the  water  during  the  process 
of  stirring.  By  repeated  experiment  it  has  been  found  that 
one  calorie  is  equivalent  to  Jj,%,730  gram-centimeters. 

Definition.  The  mechanical  equivalent  of  heat  denotes 
the  amount  of  mechanical  energy  which  must  be  transmuted 
into  heat  in  order  to  yield  one  unit  of  heat. 


THERMODYNAMICS.  305 

134.  The  Steam  Engine.  Mechanical  energy  can  be 
transformed  into  heat;  The  process  can  be  reversed ;  that 
is,  heat  can  be  transformed  into  mechanical  energy.  The 
steam  engine  is  a  contrivance  for  transforming  heat  into 
mechanical  energy.  Coal  is  burned  on  the  grate  beneath 
a  boiler  containing  water.  A  large  amount  of  the  heat  is 
wasted,  but  some  of  it  vaporizes  the  water,  turning  it  into 
steam.  This  steam  is  conveyed  to  a  cylinder,  and  is 
alternately  admitted  automatically  above  and  below  a 
piston  which  is  pushed  back  and  forth  by  the  expansion 
of  the  steam.  A  rod  attached  to  the  piston  communicates 
its  motion  to  a  wheel  which  is  kept  revolving  as  long  as 
the  piston  continues  to  move.  By  means  of  a  belt,  pass- 
ing around  this  wheel,  machinery  can  be  kept  in  motion. 


EXAMPLES. 

1.  Two  men  carry  a  weight  of  152  Ibs.  between  them  on  a  pole,  rest- 
ing on  one  shoulder  of  each  ;  the  weight  is  three  times  as  far  from  one 
man  as  from  the  other.     Find  how  many  pounds  each  supports,  the 
weight  of  the  pole  being  disregarded. 

2.  A  man  supports  two  weights  slung  on  the  ends  of  a  stick  80cm  long 
placed  across  his  shoulder.    If  one  weight  be  two-thirds  of  the  other,  find 
the  point  of  support,  the  weight  of  the  stick  being  disregarded. 

3.  A  man  carries  a  bundle  at  the  end  of  a  stick  over  his  shoulder.    As 
the  portion  of  the  stick  between  his  shoulder  and  his  hand  is  shortened, 
show  that  the  pressure  on  his  shoulder  is  increased.     Does  this  change 
alter  his  pressure  upon  the  ground  ? 

4.  If  the  forces  at  the  ends  of  the  arms  of  a  horizontal  lever  be  8  Ibs. 
and  7  Ibs.,  and  the  arms  8  in.  and  9  in.  long  respectively,  find  at  what 
point  a  force  of  1  Ib.  must  be  applied  at  right  angles  to  the  lever  to  keep 
it  at  rest. 

5.  A  uniform  rod  3  ft.  long  and  weighing  4  Ibs.  has  a  weight  of  2  Ibs. 
placed  at  one  end.     Find  the  center  of  gravity  of  the  system. 


306  EXPERIMENTAL    PHYSICS. 

6.  A  heavy  beam  is  made  up  of  two  uniform  cylinders  whose  lengths 
are  as  3  is  to  2,  and  whose  weights  are  as  3  is  to  5.     Determine  the  posi- 
tion of  the  center  of  gravity. 

7.  A  door  10  ft.  tall,  5  ft.  wide,  and  weighing  100  Ibs.  is  attached  to 
a  wall  by  one  edge  in  an  upright  position  at  two  points,  the  first  1  ft. 
above  the  bottom,  the  other  1  ft.  below  the  top.     How  great  is  the  total 
downward  pull  upon  the  wall  at  the  two  supporting  points  ?     How  great 
is  the  horizontal  force  exerted  upon  the  wall  at  each  point,  and  is  this 
force  a  push  or  a  pull  ? 

8.  A  uniform  bar  10  ft.  long  leans  with  one  end  against  a  vertical  wall 
at  an  angle  of  45°;  the  other  end  rests  upon  the  ground.    The  bar  weighs 
20  Ibs.     There  is  no  friction  between  the  bar  and  the  wall,  so  that  the 
force  there  exerted  is  entirely  horizontal.     How  great  is  this  force  ? 

9.  A  cord  is  fastened  at  each  end,  and  a  weight  is  suspended  from  it 
at  a  certain  point,  where  the  cord  bends  at  a  right  angle.     The  pull 
exerted  at  one  end  of  the  cord  is  3  pounds,  and  at  the  other  end  4  pounds. 
How  heavy  is  the  suspended  weight  ?  (The  weight  of  the  cord  is  neglected.) 

10.  A  balance  has  arms  of  unequal  length,  but  the  beam  assumes  the 
horizontal  position  when  both  scale-pans  are  empty.     Show  that  if  the 
two  apparent  weights  of  a  body  are  observed  when  it  Is  placed  first  in  one 
pan  and  then  in  the  other,  the  true  weight  will  be  found  by  multiplying 
these  together  and  taking  the  square  root. 

Solution.  Let  a  and  b  denote  the  lengths  of  the  arms  of  the  balance, 
and  x  the  true  weight  of  the  body.  If  a  weight,  101,  must  be  put  into  the 
pan  attached  to  the  arm  whose  length  is  a  when  the  body  is  put  into  the 
other  to  produce  equilibrium,  we  have,  by  the  principle  of  moments, 

bx  —  oi0i.  (I) 

If,  when  the  body  is  transferred  to  the  other  pan,  a  weight,  w%,  must 
be  put  into  the  pan  which  before  contained  the  body  to  produce  equi- 
librium, we  have 

ax  —  6w>2.  (2) 

From  (1)  a  _  x_ 

b      wi 
From  (2)  a  _  w>2 


x  = 


EXAMPLES.  307 

Hence,  the  true  weight  is  equal  to  the  square  root  of  the  product  of 
the  apparent  weights. 

11.  The  arms  of  a  balance  are  in  the  ratio  of  19  to  20 ;  the  pan  in 
which  the  weights  are  placed  is  suspended  from  the  longer  arm.     Find 
the  real  weight  of  the  body  which  apparently  weighs  38  Ibs. 

12.  Two  weights  of  2  Ibs.  and  5  Ibs.  balance  on  a  uniform  heavy  lever, 
the  arms  being  in  the  ratio  of  2  to  1.     Find  the  weight  of  the  lever. 

13.  In  a  hydraulic  (or  hydrostatic)  press  the  area  of  the  small  piston 
face  is  1  square  inch  and  that  of  the  large  piston  face  is  50  square  inches. 

(a)  If  a  force  of  50  pounds  is  applied  to  the  small  piston,  how  great  is 
the  force  exerted  upon  the  large  piston,  provided  there  be  no  friction  ? 

(6)  How  much  work  is  done  upon  the  small  piston  while  it  moves 
6  inches,  and  how  much  is  done  at  the  same  time  upon  the  large  piston  ? 
Name  the  unit  in  which  the  work  is  reckoned. 

14.  A  trap-door  of  width  4  ft.  and  weight  8  Ibs.  has  a  load  of  16  Ibs. 
applied  to  the  edge  remote  from  the  hinge. s.     How  many  foot-pounds  of 
work  will  be  done  in  raising  the  trap-door  till  the  edge  remote  from  the 
hinges  is  2  ft.  above  the  floor  ? 

15.  A  uniform  plate  of  metal  10cm  square  has  a  hole  3cm  square  cut 
out  of  it,  the  center  of  the  hole  being  2.5cm  distant  from  the  center  of  the 
plate.     Find  the  position  of  the  center  of  gravity  of  the  plate. 

16.  A  ladder,  30  ft.  long  and  weighing  48  Ibs. ,  rests  against  a  smooth 
wall,  with  its  foot  15  ft.  from  the  bottom  of  the  wall.     Find  the  pressure 
on  the  wall  and  on  the  ground,  taking  the  center  of  gravity  of  the  ladder 
as  one-third  of  its  length  up. 

17.  A  stone  is  thrown  vertically  upwards  with  a  velocity  of  192  ft.  a 
second.    Find  how  high  it  ascends,  and  how  long  it  takes  before  returning 
to  the  hand. 


CHAPTER  VII. 

MAGNETISM. 

135.  Magnets.  The  object  of  the  experiments  in  this 
article  will  be  to  make  clear  the  nature  and  the  properties 
of  magnets. 

Experiment  114.  To  find  what  happens  on  touching  a 
magnet  to  different  kinds  of  substances. 

Apparatus.  A  bar  magnet ;  bits  of  wood,  paper,  glass,  and  also 
bits  of  iron  and  copper  wire,  or  tacks. 

Directions.  Touch  one  end  of  the  magnet  to  the 
various  substances,  one  after  another-,  with  which  you 
have  provided  yourself. 

What  happens  in  each  case  ? 

The  effect  which  you  observe  on  touching  the  magnet 
to  a  bit  of  iron  is  called  attraction,  and  we  say  that  the 
magnet  attracts  the  bit  of  iron. 

Experiment  115.  To  find  whether  the  magnet  will 
attract  a  bit  of  iron  without  actually  touching  it. 

Apparatus.     A  bar  magnet  and  a  bit  of  iron. 

Directions.  Make  the  end  of  the  magnet  approach  the 
iron  very  slowly. 

Does  the  iron  move  before  the  magnet  actually  touches 
it? 

Does  the  magnet  exert  its  influence  through  the  air  ? 


POLES.  309 

Experiment  116.  To  find  whether  the  magnet  will 
attract  a  bit  of  iron  when  the  end  of  the  magnet  is  covered 
with  a  piece  of  paper. 

Apparatus.     A  bar  magnet ;  a  bit  of  iron  ;  paper. 

Directions.  Wrap  one  end  of  the  magnet  in  a  piece 
of  paper. 

Will  the  end  thus  wrapped  attract  the  iron  ? 

Experiment  117.  To  find  whether  the  attraction  of  the 
magnet  in  the  preceding  experiment  acted  through  the  paper 
or  around  it. 

Apparatus.     The  same  as  in  the  preceding  experiment. 

Directions.     Wrap  the  whole  magnet  in  paper. 

Will  the  magnet  now  attract  the  iron  ? 

Does  the  magnet  exert  its  influence  through  the  paper? 

POLES. 

136.    North-Pointing-    Pole;     South-Pointing    Pole. 

In  the  next  four  experiments  the  poles,  or  parts  of  the 
magnet  where  the  attraction  is  strongest,  will  be  found, 
as  well  as  the  direction  which  the  magnet  will  take  when 
suspended  so  that  it  can  be  free  to  turn. 

Experiment  118.  To  find  whether  the  magnet  will 
attract  at  the  center  of  its  length. 

Apparatus.     A  bar  magnet ;  an  iron  tack. 

Directions.  Touch  the  central  portion  of  the  length 
of  the  magnet  to  the  tack. 

Does  the  central  portion  of  the  magnet  attract? 


310  EXPERIMENTAL    PHYSICS. 

Experiment  119.  To  find  at  what  parts  of  a  magnet  the 
attraction  is  the  strongest. 

Apparatus.     A  bar  magnet ;  iron  filings,  fine  and  clean. 

Directions.  Lay  the  magnet  on  a  sheet  of  paper. 
Sprinkle  iron  filings  over  the  magnet ;  then  grasping  the 
magnet  in  the  middle,  carefully  raise  it  from  the  paper. 

What  portions  of  the  magnet  attract  the  strongest? 

How  does  this  experiment  enable  you  to  tell? 

How  many  poles  has  the  magnet  with  which  you  have 
experimented  ? 

Experiment  12O.  To  find  whether  one  end  of  the  mag- 
net will  point  north. 

Apparatus.     A  bar  magnet ;  a  piece  of  fine  silk  thread. 

Directions.  Tie  one  end  of  a  piece  of  thread  about  1 
ft.  long  round  the  middle  of  the  magnet.  Tie  the  free  end 
of  the  thread  to  some  support  that  will  allow  the  magnet 
to  hang  freely.  The  support  must  not  be  in  the  neighbor- 
hood of  any  iron.  Now  adjust  the  loop  round  the  magnet 
so  as  to  make  the  magnet  hang  in  a  horizontal  position. 
When  the  magnet  is  first  hung  up,  the  thread  may  twist 
a  little  and  set  the  magnet  spinning.  If  the  magnet  spins 
round  two  or  three  times,  stop  its  motion  with  the  hand, 
or  else  the  thread  will  become  twisted  the  other  way,  and, 
after  a  time,  set  the  magnet  spinning  in  the  opposite  direc- 
tion, and  thus  cause  loss  of  time. 

When  the  magnet  comes  to  rest,  does  one  end  point 
towards  the  north? 

If  so,  mark  this  end  with  a  piece  of  chalk.  Hang  the 
magnet  up  in  a  different  part  of  the  room,  but  not  in  the 
neighborhood  of  any  iron. 


ATTRACTION    AND    REPULSION.  311 

In  each  part  of  the  room  where  you  hang  the  magnet 
up,  does  the  marked  end  point  north? 

NOTE.  In  trying  experiments  with  magnets,  see  that  there  are  no 
pieces  of  iron  or  other  magnets,  in  the  neighborhood  of  the  place  where 
you  are  making  the  experiments ;  iron  weights,  retort-stands,  keys, 
knives,  etc.,  must  be  removed. 

Experiment  121.  To  find  whether  one  end  of  another 
magnet  will  point  north. 

Apparatus.     Another  bar  magnet ;  a  piece  of  fine  silk  thread. 

Directions.  Hang  up  the  new  magnet  and  repeat  with 
it  Exp.  120. 

What  is  the  result? 

If  one  end  points  north,  mark  this  end  with  chalk. 

In  a  magnet,  the  pole  that  points  north  is  called  the 
north-pointing  pole ;  the  pole  that  points  south  is  called 
the  south-pointing  pole.  We  shall  write  N-pointing  pole 
for  north-pointing  pole,  and  S-pointing  pole  for  south- 
pointing  pole. 

ATTRACTION   AND    REPULSION. 

137.    Attraction  and  Repulsion  of  Magnetic  Poles. 

We  shall  now  try  some  experiments  for  the  purpose  of 
getting  a  rule  for  predicting  whether  there  will  be  attrac- 
tions or  repulsions  when  like  poles  of  two  magnets  are 
brought  near  each  other ;  also  when  unlike  poles  are 
brought  near  each  other. 

Experiment  122.      To  find  whether  an  N-pointing  pole 
will  attract  an  N-pointing  pole. 
Apparatus.     Two  bar  magnets. 


312  EXPERIMENTAL   PHYSICS. 

Directions.  Mark  the  N-pointing  pole  of  each  magnet 
with  chalk.  Hang  up  one  of  the  magnets  as  in  Exp.  121. 
When  the  magnet  has  come  to  rest,  bring  near  its  N-point- 
ing pole  the  N-pointing  pole  of  the  other  magnet. 

What  takes  place  ? 

Experiment  123.  To  find  whether  an  S-pointing  pole 
will  attract  an  S-pointing  pole. 

Apparatus.     The  same  as  before. 

Directions.     Repeat    Exp.    122,    making    use    of    the 
S-pointing  poles  instead  of  the  N-pointing  poles. 
What  takes  place? 

Experiment  124.  To  find  whether  an  N-pointing  pole 
will  attract  an  S-pointing  pole. 

Apparatus.     The  same  as  before. 

Directions.  Repeat  Exp.  122,  but  bring  an  N-pointing 
pole  near  an  S-pointing  pole. 

What  is  the  result? 

From  the  results  of  Exps.  122,  123,  and  124,  state  a 
rule  for  predicting  what  will  take  place  when  a  pole  of 
one  magnet  is  brought  near  the  a  pole  of  another  magnet. 

138.  The  Compass.  In  the  construction  of  the  com- 
pass advantage  has  been  taken  of  the  fact  that  a  bar 
magnet,  when  suspended  in  a  horizontal  position,  points 
towards  the  north.  A  thin  piece  of  steel  that  has  been 
hardened  and  magnetized  is  poised  upon  a  fine  point  of 
hard  steel,  such  as  the  point  of  a  needle.  The  thin  piece 
of  magnetized  steel,  called  a  magnetic  needle,  will  move 
freely  round  on  this  point,  but  if  left  to  itself,  will  always 


METHOD    OF    MAKING    A    MAGNET.  313 

come  to  rest  with  its  poles  pointing  nearly  north  and 
south.  The  magnetic  needle  is  indispensable  in  naviga- 
tion, as  thereby  it  is  possible  to  ascertain  the  direction  of 
the  north  pole  of  the  earth,  and,  consequently,  to  direct 
a  vessel's  course  by  the  chart. 

METHOD    OF   MAKING   A   MAGNET. 

139.  Natural  Mag-nets ;  Artificial  Magnets.  Besides 
the  artificial  magnets  which  you  have  been  using,  there 
are  lodestones,  or  natural  magnets,  which  have  the  same 
properties  that  you  have  already  observed  in  magnets. 
The  lodestone  is  an  ore  of  iron,  black  and  hard.  This 
ore  of  iron  is  called  magnetite,  and  is  found  in  Asia  Minor, 
Sweden,  Arkansas,  and  in  other  parts  of  the  world.  The 
purpose  of  the  next  experiment  is  to  make  a  magnet. 

Experiment  125.  To  find  whether  a  magnet  can  be  made 
from  a  piece  of  steel. 

Apparatus.  A  piece  of  watch  spring  about  8cm  long;  a  bar 
magnet;  a  compass. 

Directions.  Heat  the  bit  of  watch  spring  in  a  flame 
till  it  is  just  red  hot.  Take  the  spring  from  the  flame  and 
let  it  cool.  You  will  now  be  able  to  straighten  the  spring. 
Heat  the  spring  once  more  in  the  flame,  and  when  it  is 
red  hot,  plunge  it  quickly  into  cold  water.  The  bit  of 
steel  is  now  hard  and  very  brittle. 

Stroke  the  bit  of  steel  lengthwise  with  one  pole  of  a 
strong  magnet.  Always  make  the  strokes  from  one  end 
of  the  steel,  but  never  make  back  strokes.  From  time  to 
time  turn  the  steel  so  as  to  stroke  the  other  side.  By 


314  EXPERIMENTAL    PHYSICS. 

using  the  compass,  find  which  end  of  the  little  magnet 
you  have  made  is  the  N-pointing  pole.  Keep  this  magnet 
for  the  next  experiment. 

Experiment  126.  To  find,  if  a  magnet  be  broken, 
whether  the  parts  into  which  it  is  broken  are  magnets. 

Apparatus.     The  little  magnet  you  made  in  the  last  experiment. 

Directions.     Break  the  magnet  in  the  middle. 

Is  each  part  a  magnet  ? 

By  breaking  the  magnet  thus,  have  we  succeeded  in 
separating  the.  poles  so  that  there  is  an  N-pointing  pole, 
and  an  N-pointing  pole  only,  on  one  of  the  pieces,  and  an 
S-pointing  pole,  and  an  S-pointing  pole  only,  on  the  other 
piece  ? 

Carefully  considering  what  you  have  learned  about 
magnets  from  the  experiments  you  have  performed,  give 
as  good  a  definition  as  you  can  of  a  magnet. 


MAGNETIC   INDUCTION. 

14O.  Induced  Magnetization.  Whenever  a  magnet 
by  its  action  produces  magnetization  in  a  piece  of  metal, 
this  magnetization  is  called  induced  magnetization.  The 
following  experiment  will  make  clearer  the  meaning  of 
the  term  induced  magnetization. 

Experiment  127.  To  find  what  is  meant  by  magnetic 
induction. 

Apparatus.  A  bar  magnet ;  a  short  cylinder  of  soft  iron ;  a  small 
iron  tack. 


MAGNETIC    CURVES.  315 

Directions.    Touch  the  cylinder  of  soft  iron  to  the  tack. 

Does  the  iron  attract  the  tack? 

Now  put  one  end  of  the  soft  iron  cylinder  against  one 
end  of  the  magnet,  and  holding  the  two  together,  touch 
the  other  end  of  the  soft  iron  cylinder  to  the  tack. 

Is  the  tack  attracted? 

Remove  the  magnet  from  the  soft  iron. 

What  does  the  tack  do  ? 

Put  a  piece  of  paper  between  the  end  of  the  magnet 
and  the  cylinder  of  soft  iron. 

Will  the  soft  iron  now  attract  the  tack? 

Does  the  piece  of  soft  iron  become  a  magnet  while  the 
bar  magnet  is  near  it? 

If  the  soft  iron  does  become  a  magnet,  can  you  say  it 
becomes  a  magnet  by  induction? 

MAGNETIC    CURVES. 

141.  Curves  formed  by  Iron  Filings  about  a  Mag- 
net. Whenever  iron  filings  are  sprinkled  upon  a  magnet, 
the  filings  arrange  themselves  in  clusters  at  the  poles  of 
the  magnet,  and  if  the  magnet  is  lying  on  a  table,  the 
filings,  which  fall  upon  the  table  in  the  neighborhood  of 
the  magnet,  unite  in  lines  and  assume  the  form  of  curves. 

Experiment  128.  To  find  the  general  form  of  the  curves 
of  iron  filings  sprinkled  near  a  magnet. 

Apparatua  A  bar  magnet ;  iron  filings  ;  a  muslin  bag ;  a.  sheet 
of  paper  20cm  square. 

Directions.  Lay  the  bar  magnet  on  the  table,  and  over 
it  lay  the  sheet  of  paper,  which  should  be  supported  by 


316  EXPERIMENTAL   PHYSICS. 

pieces  of  wood  so  as  to  make  the  surface  level  (meter 
sticks  are  good  for  this  purpose).  Holding  the  muslin 
bag  filled  with  iron  filings  about  a  foot  above  the  paper, 
sift  the  iron  filings  over  the  paper.  Tap  the  paper  lightly 
till  the  filings  set  themselves  along  lines.  These  lines  are 
called  magnetic  curves.  Avoid  getting  too  great  a  quan- 
tity of  filings  on  the  paper.  Sketch  in  your  note-book 
the  outline  of  the  magnet  and  the  magnetic  .curves. 

Definition.  The  space  through  which  the  magnetic  in- 
fluence of  a  magnet  extends  is  called  the  magnetic  field  of  the 
magnet. 

142.  Lines  of  Magnetic  Force.  The  preceding  ex- 
periment helps  us  to  see  what  is  meant  by  the  term 
magnetic  field.  "  This  expression  merely  denotes  the  space 
all  round  a  magnet  through  which  it  is  capable  of  exerting 
an  influence  upon  soft  iron  or  upon  other  magnets.  The 
magnetic  curves  by  which  the  magnetic  field  may  be 
mapped  out  represent,  in  the  first  place,  ropes  or  chains 
more  or  less  continuous,  into  which  the  iron  filings 
arrange  themselves  when  they  are  rendered  free  to  turn 
by  the  influence  of  tapping."  The  iron  filings,  in  fact, 
become  little  magnets  by  induction.  Had  we  used,  in- 
stead of  iron  filings,  a  series  of  very  small  magnetic 
needles  free  to  move,  these  would  have  similarly  arranged 
themselves  along  the  magnetic  curves.  These  magnetic 
curves  are  called  lines  of  magnetic  force. 

Definition.  A  line  of  magnetic  force  is  a  line  or  path  in 
a  magnetic  field,  such  that  if  we  walk  along  it  with  a  little 
magnetic  needle  suspended  from  our  hand,  this  needle  will 
always  point  along  the  path. 


MAGNETIC    CURVES.  317 

The  earth  is  a  huge  magnet  having  its  magnetic  poles 
comparatively  near  its  geographical  poles,  but  not  coinci- 
dent with  them.  The  lines  of  magnetic  force  of  the 
earth's  magnetic  field  curve  round  over  the  surface  of  the 
earth  from  pole  to  pole  and  act  on  a  freely  suspended 
magnet,  that  is,  a  magnet  that  can  turn  to  the  right  or 
left,  also  up  or  down,  in  such  a  manner  that  the  magnet 
turns  till  it  lies  as  nearly  as  possible  along  one  of  these 
lines. 

Using  a  magnetic  needle  as  suggested  in  the  definition 
of  a  line  of  magnetic  force,  we  shall  now  take  up  some 
experiments  on  tracing  lines  of  magnetic  force. 

Experiment  129.  To  find  the  shape  of  the  lines  of 
magnetic  force  about  a  bar  magnet  whose  N-pointing  pole  is 
turned  towards  theyiorth. 

Apparatus.  A  bar  magnet ;  a  small  compass ;  a  sheet  of  paper 
about  50cm  square  ;  seven  copper  tacks. 

Directions.  Fasten  the  sheet  of  paper  on  the  table 
with  copper  tacks,  not  with  iron  tacks,  at  each  corner. 
Remove  all  iron  from  the  neigborhood.  (Why?)  Draw 
a  line  extending  across  the  paper  and  pointing  north. 
This  is  done  by  laying  a  meter  stick  on  the  paper,  placing 
the  compass  on  the  stick,  and  turning  the  stick  till  the 
compass  needle  is  parallel  with  the  sides  of  the  meter 
stick.  Then  with  a  pencil  draw  a  line  beside  the  meter 
stick.  Lay  the  bar  magnet  on  the  middle  portion  of  this 
line  with  the  N-pointing  pole  pointing  north.  Fasten  the 
magnet  in  place  by  sticking  two  tacks  into  the  table  on 
one  side,  and  a  third  tack  on  the  opposite  side,  as  shown 
in  Fig.  108.  Mark  the  outline  of  the  magnet  on  the 


318  EXPERIMENTAL    PHYSICS. 

paper.  Place  the  compass  at  point  1,  Fig.  108,  of  the 
magnet,  and  then  move  it  away  in  the  exact  direction  in 
which  the  compass  needle  points.  A  good  way  to  do  this 
is  to  make  a  dot  on  the  paper  just  at  the  end  of  the 
compass  opposite  the  end  of  the  needle  that  is  turned 
away  from  the  N-pointing  pole  of  the  magnet.  Then 
move  the  compass  till  the  end  of  the  needle  that  is 
next  to  the  magnet  is  over  this  dot.  Make  a  dot  at 


FIG.  108. 

the  other  end  of  the  needle  on  the  paper,  and  continue 
this  process  till  the  path  reaches  the  edge  of  the  paper  or 
returns  to  the  magnet. 

Trace  upon  the  paper  the  lines  thus  followed  by  the 
compass,  putting  arrowheads  at  several  points  to  indicate 
the  direction  in  which  the  N-pointing  pole  of  the  compass 
needle  points  at  these  places.  Then  place  the  compass  a 
little  nearer  the  middle  of  the  magnet  (at  2),  and  starting 
anew  trace  another  line  and  mark  it  as  before.  Then, 
beginning  still  farther  (at  3)  toward  the  middle  of  the 
magnet,  do  as  before.  Finally,  start  not  more  than  3cm 
or  4cm  from  the  middle  of  the  magnet  and  trace  a  line. 
Trace  an  equal  number  of  lines  on  the  western  side  of 
the  magnet.  There  should  be  traced  in  all  eight  lines. 
Paste  the  paper  into  your  note-book. 


MAGNETIC    CUBVES. 

/•;  <. 

Experiment  13O.  To  find  the  shape  of  the  lines  of 
magnetic  force  about  a  bar  magnet  whose  N-pointing  pole  is 
turned  towards  the  south. 

Apparatua  The  same  as  in  the  last  experiment,  with  a  fresh 
sheet  of  paper. 

Directions.  Fasten  the  sheet  of  paper  to  the  table. 
Draw  a  line  across  it  towards  the  north.  Put  the  magnet 
on  the  line  and  fasten  the  magnet  with  its  N-pointing 
pole  pointing  south.  Draw  an  outline  of  the  magnet  on 
the  paper.  Then  use  the  compass  and  trace  lines  as  before, 
marking  them  all  with  arrowheads  to  indicate  the  direction 
in  which  the  N-pointing  pole  of  the  compass  needle  points. 
Start  from  the  same  points  of  the  magnet  as  in  the  last 
experiment.  Draw  eight  lines  in  all.  Paste  the  paper 
into  your  note-book. 

Experiment  131.  To  find  the  shape  of  the  lines  of 
magnetic  force  about  two  bar  magnets  placed  side  by  side, 
parallel,  and  with  their  N-pointing  poles  pointing  north. 

Apparatus.  The  same  as  in  the  last  experiment,  with  an  additional 
magnet  and  a  fresh  sheet  of  paper  and  three  more  copper  tacks. 

Directions.  Fasten  the  paper  to  the  table ;  draw  the 
line  towards  the  north ;  lay  the  two  magnets  parallel  on 
the  paper  (Fig.  109),  the  N-pointing  poles  pointing  north 
and  about  15cm  apart,  measured  on  an  east  and  west  line. 
Trace  the  outline  of  each  magnet.  Proceed  to  trace  the 
lines  of  force  as  in  the  experiments  already  performed. 
Start  from  the  positions  indicated  by  the  figures  in  the 
diagram.  Trace  the  lines  followed  by  the  compass  needle, 
and  paste  the  paper  into  your  note-book.  When  you  are 


320 


EXPERIMENTAL    PHYSICS. 


tracing  the  lines  of  force  in  the  space  between  the  magnets, 
be  careful  not  to  move  the  compass  from  the  field  of  one 
magnet  into  that  of  the  other. 

Examine  the  three  diagrams  which  you  have  made  in 


1     2     304 


FIG.  109. 

Exps.  129,  130,  and  131,  and  then  answer  the  following 
questions  : 

Is  there  any  case  in  which  all  the  lines  of  force  return 
to  the  magnet? 

Is  there  any  case  in  which  none  of  the  lines  of  force 
return  to  the  magnet? 

Is  there  any  case  in  which  some,  but  not  all,  of  the 
lines  of  force  return  to  the  magnet? 

Can  you  account  for  the  shape  of  the  lines  of  force  ? 

SUGGESTION.  Keep  in  mind  that  for  certain  positions  of  the  magnet 
the  magnet's  action  and  the  earth's  action  upon  the  compass  needle 
oppose  each  other,  while  for  other  positions  these  actions  assist  each  other. 


MAGNETIC   CUBVES. 


321 


In  the  case  where  you  had  the  two  magnets  side  by 
side,  were  the  curves  between  the  magnets  crowded  more 
closely  together  than  the  corresponding  curves  on  the 
outside  ? 

Did  you  find  in  the  case  of  the  two  magnets  a  neutral 
region,  that  is,  a  place  where  the  compass  needle  could, 
by  a  very  slight  variation  of  its  position,  be  made  to  point 
in  an  entirely  new  direction? 

143.  Theory  of  Magnetism.  Keeping  in  mind  what 
our  experiments  in  magnetism  have  taught,  let  us  try  to 
frame  a  theory  of  magnetism.  The. fact  that  lines  of  force 
leave  an  ordinary  bar  magnet  at  its  ends,  and  that  they 
also  return  to  its  ends,  might  lead  us  at  first  thought  to 
conclude  that  magnetism  exists  only  at  the  ends  of  a 
magnet ;  but  when  we  call  to  mind  the  fact  that  a  magnet 
may  be  broken  into  many  pieces  which  have  each  an 
N-pointing  pole  and  an  S-pointing  pole  of  equal  strength, 
we  infer  that,  could  we  continue  this  subdivision  of  the 
magnet  till  its  ultimate  particles,  or  molecules,  were 
reached,  each  particle  would  be  found  to  be  a  magnet 
with  an  N-pointing  pole  and  an  S-pointing  pole  of  equal 
strength.  When  to  make  a  magnet  of  a  bar  of  steel  we 
stroke  it  with  a  magnet,  we  find  that  the  magnet  loses 
none  of  its  magnetism  (it  can  lift  as  heavy  a  weight  after 
we  have  stroked  the  steel  as  before) ;  so  we  look  upon  a 
piece  of  unmagnetized  steel  as  consisting  of  particles,  each 
a  magnet  in  itself,  but  arranged  in  such  a  way  as  to 
neutralize  each  other ;  and  we  look  upon  the  process  of 
magnetization  as  consisting  in  a  rearrangement  of  the 
particles,  so  that  all  the  N-pointing  poles  shall  be  turned 


322  EXPERIMENTAL   PHYSICS. 

in  one  direction,  and  all  the  S-pointing  poles  in  the 
opposite  direction.  In  a  bar  magnet,  then,  the  layers  of 
particles  forming  the  ends  would  be  the  only  particles  the 
magnetism  of  which  is  not  completely  neutralized  by  their 
neighbors.  The  outer  face  of  the  layer  of  particles  at  one 
end  of  the  bar  would  have  free  N-pointing  magnetism ; 
the  outer  face  of  the  layer  at  the  other  end,  free  S-pointing 
magnetism. 

144.  Coercive  Force  ;  Residual  Magnetism.  A  piece 
of  hardened  steel  is  more  difficult  to  magnetize  than  a 
piece  of  soft  iron ;  but,  on  the  other  hand,  the  piece  of 
steel  retains  its  magnetism,  while  the  soft  iron  quickly 
loses  all  but  a  trace.  These  facts  are  explained  by  saying 
that  the  particles  composing  the  steel  bar  are  difficult  to 
turn  out  of  the  positions  which  they  have  when  the  bar 
is  in  its  ordinary  unmagnetized  state  ;  but  after  the 
bar  has  been  magnetized,  it  is  difficult  for  them  to  return 
into  their  old  positions,  consequently,  the  bar  of  steel 
remains  magnetized.  In  the  case  of  a  bar  of  soft  iron, 
however,  the  particles  composing  it  are  easily  turned  out 
of  their  positions ;  but  after  the  source  of  magnetization  is 
removed,  these  particles  readily  return  very  nearly  to 
their  former  positions,  and  all  but  a  trace  of  magnetism 
disappears.  The  power  of  resisting  magnetization  or 
demagnetization  is  called  coercive  force,  or  better,  reten- 
tivity.  Thus,  hardened  steel  has  great  retentivity;  soft 
iron,  little. 

The  trace  of  magnetism  that  remains  in  a  piece  of  soft 
iron,  after  its  temporary  magnetism  has  disappeared,  is 
called  residual  magnetism. 


CHAPTER    VIII. 

ELECTRICITY. 

145.  Effects  due  to  Electricity.  We  shall  begin  our 
study  of  the  subject  of  electricity  with  a  few  simple  experi- 
ments for  the  purpose  of  observing  some  of  the  effects  due 
to  electricity.  To  produce  the  electricity,  we  shall  use  a 
Bunsen  cell.  The  Bunsen  cell  is  a  contrivance  for  obtain- 
ing electricity ;  it  consists  of  the  following  parts  : 

(1)  A  glass  jar  (Fig.  110, 1),  containing  dilute  sulphuric 
acid1  to  a  depth  of  a  few  inches. 

(2)  A  hollow  cylinder  of  zinc  (Fig.  110,  2),  to  be  placed 
in  the  glass  jar. 

(3)  A  porous  cup   (Fig.  110,  3)  of  unglazed  earthen- 
ware, containing  a  mixture  of  sulphuric  acid,  water,  and 
bichromate  of  potash.2 

(4)  A  prism  of  carbon  (Fig.  110,  4),  to  be  placed  in  the 
porous  cup. 

(5)  Two  brass  clamps,  not  shown  in  the  figure.     One 
of  these  clamps  is  fastened  to  the  zinc  cylinder,  the  other 
to  the  end  of  the  carbon  prism. 

The  porous  cup  containing  the  liquid  and  the  carbon,  is 
placed  within  the  hollow  of  the  zinc  cylinder  contained 
in  the  glass  jar.  Fig.  110,  5,  represents  a  section  of  the 
cell  when  all  the  parts  have  been  brought  together  and 

1  Consisting  of  one  part  by  weight  of  sulphuric  acid  and  twelve  parts 
of  water. 

2  Consisting  of  eight  parts  by  weight  of  water,  two  parts  of  sulphuric 
acid,  and  one  part  of  bichromate  of  potash. 


324 


EXPERIMENTAL    PHYSICS. 


arranged  in  the  proper  manner.  The  different  parts 
shown  in  the  section  of  the  cell  can  be  easily  distin- 
guished by  noting  that  the  first,  the  upper,  arrow  touches 
the  glass  jar,  the  second  arrow  touches  the  zinc,  the  third 
arrow  touches  the  porous  cup,  and  the  fourth  arrow  touches 


1 


FIG.  no. 

the  carbon  prism.  The  horizontal  line  marks  the  surfaces 
of  the  liquids,  which  should  be  at  the  same  level  in  both 
the  jar  and  the  porous  cup.  Be  careful  not  to  spill  any 
of  the  acid  upon  the  clothing  or  upon  the  table. 

Experiment  132.  To  find  whether  electricity  produces 
a  physiological  effect. 

Apparatus.  A  Bunsen  cell ;  two  copper  wires,  each  about  40cm  in 
length,  with  ends  brightly  polished  with  sandpaper. 

Directions.  Attach  one  end  of  one  wire  to  the  clamp 
fastened  to  the  zinc  ;  there  is  a  little  hole  in  the  top  of 
the  clamp  into  which  the  end  may  be  slipped  and  then 
firmly  fastened  in  place  by  means  of  a  screw.  In  the 
same  manner  attach  the  end  of  the  other  wire  to  the 
clamp  which  is  fastened  to  the  carbon. 


ELECTRICITY.  325 

Touch  the  free  end  of  one  of  the  wires  to  the  tip  of  the 
tongue. 

What  is  the  sensation  ? 

Touch  the  end  of  the  other  wire  to  the  tip  of  the 
tongue,  after  removing  the  first  wire  from  the  tongue. 

What  is  the  sensation  ? 

Touch  both  wires  to  the  tongue,  so  that  the  ends  of  the 
wires  are  about  lcm  apart. 

What  is  the  sensation? 

Which  wire  seems  to  cause  the  sensation  ? 

The  sensation  you  have  felt  is  called  a  "  physiological 
effect  of  the  electric  current."  It  is  customary  to  speak 
of  electricity  as  flowing,  and  this  flow  of  electricity  is 
called  an  electric  current.  Furthermore,  the  current  is 
spoken  of  as  flowing  from  the  carbon,  through  the  wire 
joining  the  carbon,  to  the  zinc  ;  when  the  current  reaches 
the  zinc,  it  flows  through  the  liquids  in  the  cell  back  to 
the  carbon  again.  This  process  goes  on  till  the  cell 
becomes  exhausted,  by  reason  of  some  of  the  materials 
which  compose  it  becoming  used  up,  or  till  the  wire  is 
disconnected  from  either  the  zinc  or  the  carbon.  In  the 
experiment  you  have  just  performed  the  current  flowed 
through  the  tip  of  the  tongue  from  one  wire  to  the  other. 

Experiment  133.  To  find  whether  electricity  can  pro- 
duce light. 

Apparatus.  Two  Bunsen  cells  ;  three  pieces  of  copper  wire,  each 
about  40cm  long  ;  a  file. 

Directions.  By  means  of  one  of  the  wires  join  the 
zinc  of  one  cell  to  the  carbon  of  the  other.  Join  an  end 
of  one  of  the  remaining  pieces  of  wire  to  the  free  clamp  of 


326  EXPERIMENTAL   PHYSICS. 

one  cell,  and  an  end  of  the  other  wire  to  the  free  clamp 
of  the  other  cell.     To  the  end  of  either  of  the  two  wires 
last  mentioned  attach  the  file,  and  rub  the  end  of  the 
other  wire  along  the  file. 
What  do  you  see  ? 

NOTE.  An  arrangement  of  two  or  more  cells  is  called  a  battery ;  just 
as  in  military  science  a  battery  of  guns  means  an  arrangement  of  two  or 
more  guns. 

Experiment  134.  To  find  whether  the  electric  current 
can  produce  heat. 

Apparatus.  A  Bunsen  cell;  a  piece  of  iron  wire,  No.  30  B.  &  S.; 
a  piece  of  copper  wire  of  the  same  size  as  the  iron. 

Directions.  Twist  one  end  of  the  iron  wire  round  the 
end  of  one  of  the  copper  wires  leading  from  the  cell ;  then 
move  the  end  of  the  other  copper  wire  leading  from  the 
cell  along  the  iron  wire. 

Does  the  iron  wire  grow  warm  ? 

In  place  of  the  iron  wire  use  the  piece  of  copper  wire. 

Does  the  copper  wire  grow  as  warm  as  the  iron  wire  ? 

In  the  experiments  on  heat,  which  did  you  find  to  be 
the  better  conductor  of  heat,  iron  or  copper? 

If  a  poor  conductor  of  electricity  is  drawn  out  into  a 
wire  it  will  be  heated  a  good  deal. 

Hence,  which  is  the  better  conductor  of  electricity,  iron 
or  copper? 

Experiment  135.     To  find  what  effect  is  produced  on  a 
magnet  ly  an  electric  current  in  its  neighborhood. 
Apparatus.     A  Bunsen  cell ;  a  small  compass. 

Directions.  Join  the  ends  of  the  wires  leading  from 
the  cell  by  twisting  them  together.  Bring  the  loop  of 


ACTION   OF    CURRENTS    ON    MAGNETS.  327 

wire  thus  formed  close  to  the  face  of  a  compass.     What 
happens  to  the  compass  needle? 

Does  the  electric  current  act  in  any  way  like  a 
magnet  ? 

146.  The  Measurement  of  the  Strength  of  an  Elec- 
tric Current.     In  order  to  measure  the  strength  of  an 
electric  current,  you  might  make  use  of  any  one  of  the 
effects  you  have  studied  in  Exps.  132,  133,  134,  and  135, 
thus  : 

(1)  The  greater  the  physiological  effect,  the  stronger 
the  current. 

(2)  The  greater  the  luminous  effect,  the  stronger  the 
current. 

(3)  The  greater  the  heating  effect,  the  stronger  the 
current. 

(4)  The  greater  the  magnetic  effect,  the  stronger  the 
current. 

For  the  purpose  of  measuring  the  strength  of  a  current 
of  electricity  it  has  been  found  best  to  make  use  of  its 
magnetic  effect.  Hence  we  shall  make  a  careful  study 
of  the  magnetic  effect  of  the  electric  current. 

ACTION    OF    CURRENTS    ON   MAGNETS. 

147.  Magnetic  Field  produced  by  an  Electric  Cur- 
rent.    Whenever  a  current  of  electricity  flows  through 
a  conductor,  a  magnetic  field  is  produced,  by  the  current, 
in  the  neighborhood  of   the  conductor.     It  will  be  our 
purpose  to  find  out  something  about  the   lines  of  force 
in  a  magnetic  field  which  is  produced  in  this  way. 


328  EXPERIMENTAL   PHYSICS. 

Experiment  136.  To  find  the  shape  of  the  lines  of  force 
when  a  magnetic  field  is  produced  in  the  neighorhood  of  a 
conductor  by  a  current  of  electricity  flowing  through. 

Apparatus.  Two  Bun  sen  cells ;  a  stout  copper  wire ;  a  piece  of 
cardboard  about  20cm  square  ;  fine  iron  filings  ;  pieces  of  copper  wire 
for  connecting  the  cells. 

Directions.  Join  the  zinc  of  one  cell  to  the  carbon  of 
the  other  by  a  piece  of  wire.  Pierce  the  cardboard  at  its 
center  with  a  hole  large  enough  for  the  stout  wire  to  pass 
through.  Place  the  cardboard  in  a  horizontal  position 
with  the  stout  wire  protruding  vertically  through  the  hole 
both  above  and  below.  To  one  end  of  this  stout  wire 
join,  by  means  of  a  piece  of  wire,  the  free  carbon,  and  to 
the  other  end  of  the  stout  wire,  also  by  means  of  a  piece 
of  wire,  join  the  free  zinc.  A  current  is  now  flowing 
through  the  stout  copper  wire.  Sprinkle  on  the  card- 
board a  few  iron  filings,  and  gently  tap  the  cardboard. 

In  what  form  do  the  filings  arrange  themselves  on  the 
cardboard  ? 

What  is  the  form  of  the  lines  of  force  in  the  magnetic 
field  surrounding  the  conductor? 

Experiment  137.  To  find  the  relation  between  the 
direction  of  the  electric  current  and  the  direction  in  which  a 
compass  needle  points,  when  placed  in  the  neighborhood  of 
the  current. 

Apparatus.  A  Bunsen  cell ;  a  compass  ;  a  piece  of  copper  wire 
2m  or  3m  long  ;  two  connecting  cups ;  five  copper  tacks. 

Directions.  Bend  the  piece  of  wire  into  the  form  of  a 
square  (Fig.  Ill),  and  have  the  ends  of  the  wire  project 


ACTION   OF   CURRENTS    ON   MAGNETS.  329 

5cm  or  10cm  from  the  corner  of  the  square.  Place  this 
square  on  the  table  so  that  two  sides  shall  run  east  and 
west,  and  the  other  two  north  and  south.  You  can  make 
sure  that  the  square  is  placed  correctly  by  means  of  a 
compass,  adjusting  the  square  till  the  sides  that  are  to  run 
north  and  south  are  parallel  to  the  needle.  Join  (Fig.  Ill), 
by  means  of  connecting  cups,  the  ends  of  the  wire  forming 
the  square  to  the  ends  of  the  wires  from  the  cell.  Be  care- 
ful to  scrape  the  insulating  material  from  the  ends  of  the 
wires,  in  order  to  get  good  contact.  Fasten  the  corners 
of  the  square  to  the  table  with  cop- 
per tacks.  The  figure  represents 
the  arrangement.  The  arrowheads 
denote  the  direction  in  which  the 
current  flows  in  going  from  the 
carbon  of  the  cell  through  the  wire 
back  to  the  zinc  of  the  cell.  Call 

the  side  of  the  square  through  which  the  current,  on  its 
way  from  the  carbon  to  the  zinc,  flows  east,  E,  that  in 
which  it  flows  west,  W,  etc. 

Draw  in  your  note-book  a  diagram  similar  to  the  figure. 
Now  place  the  compass  on  the  wire  at  the  middle  of  the 
side  E,  and  indicate,  by  drawing  a  straight  line  through 
the  middle  point  of  the  line  E  in  your  note-book,  the 
general  direction  in  which  the  N-pointing  pole  of  the 
compass  needle  turns.  At  one  end  of  this  line  put  an 
arrowhead,  to  show  which  end  represents  the  N-pointing 
pole  of  the  needle. 

Now  draw  another  diagram  in  your  note-book  just  like 
the  one  you  have  already  drawn.  Lift  the  wire  a  little 
way  on  the  side  E,  without  detaching  it  from  its  fasten- 


330  EXPERIMENTAL    PHYSICS. 

ings,  and  slip  the  compass  underneath  the  middle  of  the 
side  JE.  In  the  new  diagram,  by  drawing  a  line  as  before, 
indicate  the  direction  in  which  the  needle  points.  Do  the 
same  thing  with  each  of  the  sides  $  W,  and  JV,  marking 
in  one  diagram  the  position  of  the  needle  when  placed 
above  the  middle  point  of  each  side,  and  in  the  other 
diagram  the  position  of  the  needle  when  the  compass  is 
placed  beneath  the  middle  point  of  each  side. 

QUESTIONS. 

By  referring  to  your  diagrams,  answer  the  following  questions : 

1.  A  wire  is  stretched  north  and  south,  and  a  current  runs  from  south 
to  north  in  the  wire ;   if  a  compass  is  placed  above  the  wire,  will  the 
N-pointing  pole  of  the  needle  be  on  the  east  or  on  the  west  side  of  the 
wire  ? 

2.  Suppose  the  conditions  mentioned  in  1  remain  the  same  in  all 
respects,  except  that  the  compass  is  placed  under  the  wire ;  on  which  side 
(east  or  west)  will  the  N-pointing  pole  of  the  needle  lie  ? 

3.  Suppose  all  the  conditions  mentioned  in  1  remain  unchanged, 
except  that  the  current  flows  from  north  to  south ;  what  will  be  the  posi- 
tion of  the  N-pointing  pole  of  the  needle  ? 

4.  If  in  the  last  question  the  compass  had  been  placed  under  the  wire, 
everything  else  remaining  the  same  as  before,  what  position  would  the 
N-pointing  pole  of  the  needle  have  taken  ? 

5.  In  a  wire  stretched  east  and  west  a  strong  current  of  electricity 
flows  from  east  to  west ;  if  a  compass  is  placed  above  the  wire,  will  the 
N-pointing  pole  turn  to  the  north  or  to  the  south  side  of  the  wire  ? 

6.  Suppose  all  the  conditions  of  5  remain  unchanged,  except  that  the 
compass  is  placed  underneath  the  wire ;  what  position  does  the  N-pointing 
pole  of  the  needle  take  ? 

7.  Suppose  all   the   conditions  mentioned   in   5  remain  unchanged, 
except  that  the  current  flows  from  west  to  east ;  in  what  position  will 
the  N-pointing  pole  of  the  compass  needle  point  ? 

8.  Suppose   all   the   conditions  mentioned  in  7  remain  unchanged, 
except  that  the  compass  is  placed  below  the  wire ;  what  position  will  the 
N-pointing  pole  of  the  needle  now  take  ? 


LINES   OF   FORCE   ABOUT   A   COIL.  331 

148.  Rule  for  Direction  of  Deflection  of  Magnetic 
Needle  by  Electric  Current.  A  line  of  force  is  said  to 
have  the  direction  in  which  the  N-pointing  pole  of  a  com- 
pass needle  points,  when  placed  on  the  line  of  force  ; 
bearing  this  in  mind,  answer  the  following  question  : 

If  you  look  along  the  wire  in  the  direction  in  which 
the  current  flows,  will  the  lines  of  force  run  round  the 
wire  in  the  same  direction  as  the  hands  of  a  clock  move? 

Your  answer  to  this  question  gives  the  rule  for  finding 
the  direction  of  deflection  of  a  magnetic  needle  by  an 
electric  current. 

LINES    OF   FORCE   ABOUT   A    COIL. 

Experiment  138.  To  find  the  positions  of  the  lines  of 
force  surrounding  a  conductor  which  consists  of  a  coil  of  wire. 

Apparatus.  A  wooden  ring,  round  which  is  wound  15  turns  of 
insulated  copper  wire,  mounted  on  a  base  (this  wire  is  wound  with 
cotton  or  silk  to  keep  the  electricity  from  going  across  from  one  spire 
to  the  next ;  a  wire  thus  covered  is  called  insulated  wire) ;  a  Bunsen 
cell ;  a  compass  ;  a  meter  stick. 

Directions.  To  each  of  the  outer  binding  posts  join  a 
wire  from  the  cell  (Fig.  112).  By  counting  the  coils  of 
wire  you  can  assure  yourself  that  there  are  15  turns  on  the 
wooden  ring,  and  by  carefully  examining  the  apparatus  you 
will  see  that  there  are  15  turns  of  wire  "  in  circuit,"  which 
is  a  brief  form  of  saying  that  all  these  15  turns  of  wire  are 
traversed  by  the  current.  Place  the  ring  so  that  the  plane 
of  its  coil  shall  be  east  and  west,  and  so  that  the  current 
shall  flow  from  east  to  west  through  the  wires  on  the  top 
of  the  circle.  To  find  whether  the  current  is  flowing  in 


332  EXPERIMENTAL   PHYSICS. 

the  way  described,  place  the  compass  on  the  top  of  the 
circle,  observe  the  position  of  the  needle,  and  refer  to  the 
rule  about  the  deflection  of  a  magnetic  needle  which  you 
were  asked  to  state.  On  the  cross-piece  place  a  meter 
stick  with  its  center  on  that  of  the  cross-piece,  and  have 
the  meter  stick  at  right  angles  to  the  plane  of  the  coil. 
Support  the  ends  of  the  meter  stick  by 
means  of  blocks  to  keep  the  stick  steady. 
The  stick  should  be  pointing  north  and 
south.  On  the  meter  stick  place  the 
compass  10cm  south  of  the  center  of  the 
coil,  and  record  in  a  diagram,  by  means 
of  a  straight  line,  the  direction  in  which 
the  needle  points.  Now  move  the  com- 
pass north  along  the  meter  stick  5cm;  record  as  before  the 
position  of  the  needle.  Then  move  the  compass  5cm  north 
to  the  center  of  the  coil ;  record.  Again  move  the  compass 
5cm  north ;  record.  Finally,  move  the  compass  5cm  north 
from  the  last  stopping-place,  and  record  the  position  of 
the  needle. 

Place  the  compass  within  the  coil,  but  close  to  its  east- 
ern side.  Record,  by  means  of  a  diagram,  the  direction 
of  the  needle.  Then  place  the  compass  in  turn  north, 
east,  and  south  of  this  portion  of  the  coil  (and  all  the  time 
close  to  it),  recording  the  direction  in  which  the  needle 
points  for  each  position  of  the  compass.  Carrying  the 
compass  round  the  western  side  of  the  coil,  make  and 
record  similar  observations.  Fig.  113  may  help  to  make 
the  meaning  of  this  paragraph  clearer.  The  shade  lines 
represent  the  part  around  which  the  compass  is  carried ; 
the  circles,  the  positions  of  the  compass. 


o  +  o 


o       o 


CHEMICAL    ACTION    IN    THE    CELL.  333 

Now  reverse  the  current  in  the  coil.  This  is  done  by 
changing  the  connections  with  the  cell,  putting  the  wire 
attached  to  the  zinc  in  the  binding  post  that  before  held 
the  wire  from  the  carbon,  and  the  wire  from  the  carbon 
into  the  binding  post  that 
before  held  the  wire  from  the 
zinc.  Repeat  all  the  opera- 
tions described  in  the  preced- 
ing part  of  this  experiment,  (j|[)  Cj  J 
and  make  new  diagrams. 

Compare   the   diagrams  ob- 
tained by  moving  the  compass 

/  FIG.  113. 

round  the  east  and  west  sides 

of  the  coil  with  those  obtained  in  Exp.  131  in  magnetism, 
when  the  two  magnets  were  placed  parallel  to  each  other. 
In  this  comparison,  point  out  the  differences  and  the  like- 
nesses in  the  arrangement  of  the  lines  of  force  about  the 
magnets  and  about  the  coil. 

In  this  experiment,  have  you  noticed  anything  in  the 
course  of  your  work  that  would  make  it  appear  as  if  the 
coil  acted  as  a  magnet,  having  one  pole  at  one  face  of 
the  coil  and  the  other  pole  at  the  other  face  ? 


CHEMICAL    ACTION    IN    THE    CELL. 

149.   Study  of  the  Action  that  takes  Place  in  the  Cell. 

As  we  have  now  studied  some  of  the  effects  of  electricity, 
we  are  in  a  better  position  to  study  the  action  that  goes 
on  in  the  cell.  In  beginning  the  study  of  the  cell,  we 
shall  take  the  simplest  form,  not  the  complicated  arrange- 
ment that  we  have  been  using. 


334  EXPERIMENTAL   PHYSICS. 

Experiment  139.  To  find  what  action  dilute  sulphuric 
acid  has  upon  a  strip  of  zinc  and  upon  a  strip  of  copper 
placed  in  it. 

Apparatus.  A  small  glass  tumbler ;  a  strip  of  sheet  zinc  and  a 
strip  of  sheet  copper,  each  about  10cm  long  and  1.5cm  wide,  and  each 
having  about  50cm  of  insulated  copper  wire  (size  about  No.  20  B.  &  S.) 
soldered  to  one  end. 

Directions.  At  the  sink,  fill  the  tumbler  to  within  lcm 
of  its  top  with  dilute  sulphuric  acid  (1  part  by  volume  of 
acid  to  20  parts  by  volume  of  water).  Do  not  let  any  of 
the  acid  fall  upon  the  floor,  table,  or  clothing.  Put  into 

the  tumbler,  close  to  one  side,  the 
strip  of  clean  zinc,  and  close  to 
the  other  side  the  similar  strip  of 
copper;  each  strip  should  rest  on 
the  bottom  of  the  tumbler,  and 
the  upper  end  of  each  should  be 
Fio  j  bent  so  as  ,to  clasp  the  edge  of 

the    tumbler,  as    shown  in  Fig. 

114.  Now  observe  for  about  a  minute  what  happens  at 
the  surface  of  each  strip,  taking  care  that  the  strips  do  not 
touch  each  other. 

What  happens  at  the  surface  of  each  strip  ? 

Experiment  14O.  To  find  what  happens  when  a  strip- 
of  zinc  and  a  strip  of  copper,  plunged  into  dilute  sulphuric 
acid,  are  joined  by  a  piece  of  copper  wire. 

Apparatus.  The  same  as  in  the  preceding  experiment;  also  a 
compass  and  a  coil  mounted  on  a  base  as  shown  in  Fig.  112;  mercury. 

Directions.  Having  the  tumbler,  plates,  and  acid 
arranged  as  in  the  last  experiment,  put  the  two  strips  into 
metallic  connection,  by  attaching  their  wires  to  the  ends 


CHEMICAL    ACTION    IN    THE   CELL.  335 

of  the  15-turn  coil.  Before  the  wires  are  attached,  how- 
ever, the  compass  should  be  placed  on  the  center  of  the 
shelf  running  across  the  coil,  and  the  coil  turned  round 
till  the  needle  of  the  compass  lies  in  the  plane  of  the  coil. 
The  little  instrument  thus  arranged,  consisting  of  the 
compass  and  the  coil,  is  called  a  galvanoscope.  It  enables 
us  to  detect  the  presence  of  an  electric  current;  for,  as 
we  already  know,  if  a  current  flows  through  the  coil,  the 
needle  is  deflected  from  its  natural  position ;  if  the  current 
is  strong,  the  needle  will  be  deflected  a  good  deal ;  if  the 
current  is  weak,  the  needle  will  be  deflected  only  a  little. 
Whenever  the  galvanoscope  is  used,  it  must  be  placed  in  a 
position  to  make  its  coil  lie  in  the  magnetic  meridian;  that 
is,  the  needle  of  the  compass  on  the  little  shelf  running 
through  the  center  of  the  cx)il  must  lie  in  the  plane  of  the 
coil.  After  the  galvanoscope  has  been  placed  in  position,  on 
no  account  must  its  position  be  changed  till  the  experiment  is 
completed. 

Observe  for  a  short  time  what  happens  at  the  surface  of 
each  of  the  strips  in  the  acid. 

Do  any  bubbles  form  and  rise  ?  Do  more  rise  from  one 
strip  than  from  the  other? 

Observe,  too,  the  behavior  of  the  galvanoscope  needle. 

After  tapping  the  instrument  lightly  to  make  sure  that 
the  needle  has  not  through  friction  on  the  pivot  come  to 
rest  in  the  wrong  position,  record  the  number  of  degrees 
through  which  the  tip  of  the  needle  has  turned. 

Disconnect  the  zinc  strip,  and  plunge  into  mercury  that 
part  only  which  has  been  under  the  acid.  Then,  after 
wiping  from  the  zinc  any  loose  drops  of  mercury,  replace 
it  in  the  acid. 


336  EXPERIMENTAL   PHYSICS. 

What  happens  now  at  the  surface  of  the  zinc  ? 
Now  connect,  as  before,  with  the  galvanoscope. 
What  happens  at  the  surface  of  the  zinc  ? 
Be   careful  that  the   two  strips  are  as   far  apart  and 
immersed  to  the  same  depth  as  before. 

What  position  does  the  galvanoscope  needle  take  ? 
What  happens  at  the  surface  of  the  copper  strip  ? 

Experiment  141.  To  find  whether  the  strength  of  the 
current  from  the  single-fluid  cell  changes  as  time  goes  on. 

Apparatus.     The  same  as  in  the  last  experiment. 

Directions.  Wipe  the  plates  dry  and  clean.  Then 
put  them  into  the  liquid  and  immediately  get  the  reading 
of  the  galvanoscope,  that  is,  the  number  of  degrees  through 
which  the  N-pointing  pole  of  the  needle  is  deflected. 
Readings  should  then  be  taken  every  two  minutes  for  a 
period  of  ten  minutes.  If  at  the  end  of  ten  minutes  there 
are  any  bubbles  on  either  of  the  strips  or  on  both,  rub  off 
these  bubbles  with  a  bit  of  wood  without  removing  the 
strips  from  the  acid,  talcing  care  to  have  no  mercury  come  in 
contact  with  the  copper.  Record  the  position  of  the  needle 
in  every  case. 

Finally,  try  the  effect  of  amalgamating  (covering  with 
mercury)  the  copper ;  the  zinc  has  been  amalgamated. 

How  do  you  account  for  the  position  of  the  needle  ? 

15O.  Discussion  of  the  Chemical  Action  that  takes 
Place  in  the  Cell.  Chemists  teach  that  a  molecule  of  sul- 
phuric acid  consists  of  two  parts  of  hydrogen  (the  bubbles 
that  you  saw  rising  from  the  zinc  before  the  circuit  was 
closed  were  bubbles  of  hydrogen),  one  part  of  sulphur, 


CHEMICAL    ACTION    IN    THE    CELL.  SB 7 

and  four  parts  of  oxygen.  When  this  molecule  of  sul- 
phuric acid  comes  in  contact,  under  proper  conditions, 
with  zinc,  chemical  action  takes  place  and  the  two  parts 
of  hydrogen  in  the  molecule  are  pushed  or  crowded  out 
by  one  part  of  zinc,  and  the  hydrogen  passes  off  in  the 
form  of  bubbles,  while  the  compound  formed  with  the  zinc 
remains  behind ;  this  compound  is  called  zinc  sulphate. 

151.  The  Reason  for  Amalgamating  the  Zinc.     If 

the  zinc  is  acted  upon  by  the  acid  when  the  battery  is 
not  in  use,  a  waste  of  zinc  takes  place ;  pure  zinc,  when 
placed  in  sulphuric  acid,  is  but  little  affected.  Pure  zinc, 
however,  is  expensive,  so  we  use  impure,  but  amalga- 
mated, zinc.  Impure  zinc  when  amalgamated  behaves  in 
sulphuric  acid  much  like  pure  zinc;  the  mercury  dissolves 
the  zinc,  leaving  the  impurities  unchanged,  thus  spread- 
ing a  coating  of  pure  zinc  over  the  surface  of  the  plate. 

Under  ordinary  circumstances,  sulphuric  acid  acts  but 
slightly  upon  copper.  Any  action  seen  at  the  surface  of 
the  copper  strip  in  Exp.  140,  even  when  the  circuit  was 
closed,  was  due  to  hydrogen  bubbles,  set  free  by  a  chem- 
ical action  that  did  not  affect  the  copper. 

152.  Polarization  of  the  Cell.     The  weakening  of  the 
current  of  a  single-fluid  cell  after  the  circuit  is  closed, 
and    the    recovery    of    strength    by    the    current    when 
the  plates  are    thoroughly  rubbed,   are    phenomena  that 
demand  our  attention.     This  weakening  of  the  current  is 
evidently  not  due  to  an  exhaustion  of  the  fluids  in  the 
cell,  but  rather  to  the  condition  produced  at  the  surface 
of  one  or  both  of  the  metallic  strips  by  the  action  of  the 
cell.     In  fact,  the  weakening  of   the  current  is  due  to 


338  EXPERIMENTAL    PHYSICS. 

the  deposition  of  bubbles  of  hydrogen  upon  the  plate  of 
copper ;  for  when  the  bubbles  are  removed,  the  strength 
of  the  current  returns.  This  deposition  of  hydrogen 
bubbles  upon  the  copper  plate  is  called  polarization  of 
the  cell.  The  coating  of  hydrogen  bubbles  upon  the  plate 
acts  in  two  ways  to  weaken  the  current : 

(1)  Since  the  hydrogen  is  a  poor  conductor  of  elec- 
tricity, it  opposes  the  flow  of  the  current ; 

.  (2)  When  the  copper  strip  is  covered  with  a  film  of 
hydrogen,  we  have  practically  a  plate  of  hydrogen  exposed 
to  the  action  of  the  acid;  the  result  is  the  starting  of  a 
current  in  the  opposite  direction,  that  tends  to  neutralize 
the  first,  which  flows  in  the  cell  from  the  zinc  to  the 
copper.  The  more  the  copper  plate  gets  covered  with 
the  hydrogen  bubbles,  the  stronger  does  this  neutralizing 
tendency  become,  until  the  first  current  is  overpowered ; 
then  the  galvanoscope  indicates  no  current  in  either  direc- 
tion. 

In  order  to  avoid  the  formation  of  hydrogen  bubbles 
upon  the  copper  plate,  use  is  made  of  the  two-fluid  cell. 
In  this  cell  the  copper  plate  is  immersed  in  a  liquid 
which  does  not  allow  hydrogen  to  reach  the  copper  plate. 
Just  how  this  is  done  will  become  clearer  after  perform- 
ing the  following  experiment  with  a  two-fluid  cell. 

Experiment  142.  To  find  what  action  goes  on  in  the 
two-fluid  cell. 

Apparatus.  A  large  tumbler ;  a  small  porous  cup  that  will  sit 
easily  into  the  tumbler ;  a  piece  of  zinc  10cm  long,  2.5cm  wide,  0.4cm 
thick,  with  a  piece  of  copper  wire  40 cm  long  soldered  to  it ;  a  piece  of 
sheet  copper  10cm  square,  with  a  copper  wire  40cm  long  like  that  of 


CHEMICAL    ACTION    IN   THE    CELL.  339 

the  zinc ;  a  galvanoscope ;  dilute  sulphuric  acid  (one  part  by  volume 
of  acid  to  twenty  parts  by  volume  of  water);  a  saturated  solution  of 
sulphate  of  copper  ;  mercury. 

Directions.  Put  the  zinc  into  the  porous  cup,  and  then 
fill  this  cup  with  diluted  sulphuric  acid  to  within  2cm  of 
its  top.  Put  the  cup  containing  the  zinc  and  acid  into 
the  tumbler,  and  then  pour  into  the  tumbler  sulphate  of 
copper  solution  till  this  liquid  stands  as  high  in  the  tum- 
bler as  the  acid  stands  in  the  porous  cup.  Then  remove 
the  zinc  from  the  acid.  The  zinc  is  now  in  a  condition  to 
be  amalgamated,  which  should  be  done  by  dipping  it  into 
the  mercury.  After  amalgamation,  wipe  the  zinc  to  re- 
move loose  drops  of  mercury  (do  this  over  an  iron  pan  to 
save  the  mercury),  and  then  weigh  the  amalgamated  zinc 
to  O.lgm.  Wash,  dry,  and  then  weigh  with  equal  accuracy 
the  copper  sheet.  Bend  the  copper  plate  somewhat  so 
that  it  may  partly  encircle  the  porous  cup,  and  put  the 
plate  thus  bent  into  the  sulphate  of  copper  in  the  tum- 
bler. Replace  the  zinc  in  the  porous  cup.  You  already 
know  that  if  one  wire  from  a  cell  is  joined  to  one  of  the 
outside  posts  of  the  galvanoscope  and  the  other  wire  from 
the  cell  to  the  other  outside  binding-post,  then  the  current 
from  the  cell  will  flow  through  15  turns  of  the  galvano- 
scope coil.  On  the  other  hand,  if  one  of  the  wires  from 
the  cell  is  joined  to  the  middle  post  and  the  other  wire 
to  one  of  the  outside  posts,  the  current  from  the  cell  will 
flow  through  5  or  10  turns  of  the  galvanoscope  coil,  ac- 
cording to  which  of  the  outer  posts  the  wire  is  attached  to. 
Join  the  cell  to  the  galvanoscope  so  that  the  current  shall 
flow  through  the  5-turn  section.  As  soon  as  the  needle 
comes  to  rest  (before  reading  the  instrument,  it  should  be 


340  EXPERIMENTAL   PHYSICS. 

lightly  tapped  so  that  the  needle  may  disengage  itself  if 
caught  by  friction  on  the  pivot),  record  its  position,  stat- 
ing how  many  degrees  it  is  deflected  from  the  magnetic 
meridian,  and  also  whether  this  deflection  is  towards  the 
east  or  towards  the  west.  Readings  should  be  taken  and 
recorded  at  5-minute  periods  for  half  an  hour.  Then  dis- 
connect the  cell,  remove  both  the  zinc  and  the  copper, 
rinse  each  gently,  taking  care  not  to  remove  any  deposit 
that  may  have  formed ;  and  then,  without  rubbing,  dry 
the  plates,  and  weigh  them  again. 

What  has  been  the  gain  or  loss  in  weight  for  each 
plate? 

From  an  inspection  of  the  record  of  the  galvanoscope 
readings,  should  you  say  that  the  current  had  become 
and  remained  constant  soon  after  the  beginning  of  the 
experiment? 

At  the  beginning  of  the  experiment  the  walls  of  the 
porous  cup  are  often  not  thoroughly  wet.  After  a  little 
while,  however,  the  liquids  soak  in  and  the  walls  become 
moist.  The  current  flows  more  easily  through  a  substance 
thoroughly  wet  than  through  the  same  substance  when 
only  moist. 

NOTE.  This  two-fluid  cell  with  which  you  have  experimented  is 
called,  from  the  name  of  its  inventor,  the  Daniell  cell. 

153.  Chemical  Action  in  the  Two-Fluid  Cell.  With- 
in the  porous  cup,  in  Exp.  142,  the  zinc  pushes  out  the 
hydrogen  in  the  sulphuric  acid  and  takes  its  place. 
The  hydrogen  thus  set  free  does  not  appear  in  the  form 
of  bubbles,  but  in  the  part  of  the  cell  outside  the  porous 
cup,  it  pushes  out  the  copper  of  the  copper  sulphate 


CHEMICAL    ACTION    IN   THE   CELL.  341 

(copper  sulphate  consists  of  1  part  of  copper,  1  of  sul- 
phur, and  4  of  oxygen).  The  copper  freed  in  this  manner 
is  deposited  upon  the  copper  plate.  Instead  of  hydrogen 
being  deposited  upon  the  copper  plate,  copper  is  depo- 
sited and  polarization  is  prevented.  The  cell  gives  a 
steady  current  till  the  materials  (generally  the  copper 
sulphate)  of  the  cell  become  exhausted.  The  Bunsen1 
cell  is  a  two-fluid  cell. 

154.  The  Ampere.     Exp.  142  gives  a  means  of  under- 
standing clearly  what  is  meant  by  the  ampere,  the  unit  of 
current  strength. 

Definition.  An  ampere  is  a  current  of  such  strength  as 
to  set  free  from  its  chemical  combinations  0-0003281  of  a 
gram  of  copper  in  one  second. 

The  usual  strength  of  current  for  an  arc-lamp  is  about 
10  amperes. 

Turn  back  to  your  record  of  Exp.  142,  and  with  the  data 
there  furnished,  compute  the  weight  in  grams  of  copper  set 
free  (that  is,  deposited  on  the  copper  plate)  from  the  sul- 
phate of  copper  solution  in  one  second  by  the  current. 

If  a  current  of  one  ampere  sets  free  in  one  second 
0.00032818  °f  copper  from  its  chemical  combinations,  what 
was  the  average  strength  in  amperes  of  the  current  pass- 
ing through  your  Daniell  cell  during  the  half-hour  test? 

155.  The  Commutator;  the  Rheostat.     In  the  next 
experiment   you   will    have   occasion   to    use    two   pieces 

1  It  is  better  to  call  the  cell  you  used  in  the  first  experiments  in  elec- 
tricity the  Poggendorff  cell.  The  true  Bunsen  cell  has  nitric  acid  in  the 
porous  cup  instead  of  the  mixture  of  water,  sulphuric  acid,  and  bichro- 
mate of  potash  which  you  used. 


342  EXPERIMENTAL    PHYSICS. 

of  apparatus,  a  description   of  which  is  here  given  for 
convenience. 

Hitherto,  when  you  wished  to  change  the  direction  of 
a  current  through  a  conductor  (the  galvanoscope  coil,  for 
instance),  the  ends  of  the  wires  from  the  cell  were  inter- 
changed at  the  ends  of  the  conductor.  This  changing  of 
connections  was  troublesome  and  took  time.  To  effect 
this  change  quickly  and  conveniently,  a  piece  of  apparatus 
called  a  commutator  has  been  contrived. 

The  commutator  (Fig.  115)  consists  of  a  block  of  wood 
in  one  side  of  which  four  holes,  called  cups,  are  made. 
There  are  four  binding-posts  screwed 
into  tlie  sides  of  the  block,  one  enter- 
ing each  cup.  The  cups  are  partly 
filled  with  mercury.  There  are  also 
two  wires  passing  through  a  disc  of 
wood  and  bent  at  the  ends,  by  means 

of  which  the  cups  can  be  connected  in 
no.  115.  pairs> 

The  cell  must  always  be  joined  to  a  pair  of  opposite 
binding-posts,  and  the  galvanoscope  wires  must  be  joined 
to  the  other  pair  of  binding-posts. 

If  the  set  of  movable  wires,  carried  by  the  wooden  disc, 
dip  into  the  cups,  the  current  flows  from  the  cell  through 
the  galvanoscope.  If  the  disc  is  raised,  given  a  quarter 
turn  and  then  lowered,  the  current  will  flow  in  the  op- 
posite direction  through  the  galvanoscope. 

The  rheostat,  shown  in  the  upper  part  of  Fig.  116,  con- 
sists of  a  frame  made  by  attaching  an  upright  at  each  end 
of  a  piece  of  plank  about  a  meter  long,  and  joining  the 
upper  ends  of  these  uprights  by  a  meter  stick  parallel  to 


ELECTRICAL    RESISTANCE.  343 

the  plank.  On  one  of  the  uprights  are  placed  four  hori- 
zontal rows  of  binding-posts.  Each  row  consists  of  two 
posts.  On  the  other  upright,  near  its  lower  end,  is  placed 
a  horizontal  row  of  two  binding-posts.  Between  the  two 
uprights  is  stretched  a  piece  of  No.  30  German  silver 
wire,  held  in  place  at  its  ends  by  the  binding-posts  which 
are  nearest  the  plank  and  are  placed  nearest  the  inside 
edge  of  each  upright.  Another  piece  of  No.  30  German 
silver  wire  is  fastened  to  the  outer  binding-post  of  the 
lowest  row.  This  wire  is  then  carried  round  the  outer 
edge  of  the  upright  and  brought  to  the  other  upright 
round  whose  outer  edge  it  is  carried  and  fastened  to  the 
binding-post  nearest  this  edge.  Another  piece  of  No.  30 
German  silver  wire  is  fastened  to  one  of  the  binding-posts 
in  the  next  row  above,  is  carried  once  round  the  supports, 
and  fastened  at  its  end  to  the  other  binding-post  of  the 
pair.  The  same  thing  is  done  for  the  next  pair  of  posts, 
only  a  No.  28  German  silver  wire  is  used.  Finally,  round 
the  upper  part  of  the  rack  are  wrapped  20m  of  silk-cov- 
ered, No.  30,  copper  wire  ;  an  end  of  this  wire  terminates 
at  each  of  the  upper  pair  of  binding-posts. 


ELECTRICAL    RESISTANCE. 

156.  Electrical  Resistance  of  Wires.  When  water 
runs  through  a  pipe,  the  friction  between  the  walls  of 
the  pipe  and  the  flowing  water  resists  the  flow.  The 
current  of  water  is  not  so  strong  as  it  would  be  were 
the  impeding  effect  of  friction  removed.  The  resistance 
to  a  flow  of  water  in  two  pipes  of  the  same  diameter,  but 
of  unequal  lengths,  is  greater  in  the  longer  pipe.  On 


344  EXPERIMENTAL    PHYSICS. 

the  other  hand,  in  two  pipes  of  the  same  length,  but  of  un- 
equal diameters,  the  resistance  is  greater  in  the  smaller. 

Thus,  just  as  a  pipe  through  which  water  runs  offers 
to  the  flow  a  resistance,  which  depends  upon  the  size  and 
length  of  a  pipe,  so  a  wire  offers  resistance  to  the  flow  of 
electricity.  It  will  be  the  object  of  the  next  two  experi- 
ments to  find,  if  possible,  some  relation  between  the  length 
of  the  wire  and  the  amount  of  resistance  (Exp.  143);  also 
between  the  area  of  cross-section  of  the  wire  and  the 
amount  of  resistance  (Exp.  144). 

Experiment  143.  To  find  what  effect  the  length  of  a 
wire  has  upon  its  resistance  to  the  flow  of  an  electric  current. 

Apparatus.  A  Daniell  cell ;  a  rheostat ;  a  commutator  ;  a  gal- 
vanoscope  ;  an  "  English  "  binding-post. 

Directions.  By  means  of  a  bit  of  copper  wire  connect 
the  pair  of  binding-posts  at  the  bottom  of  the  left-hand 
upright  (Fig.  116) ;  thus  the  two  pieces  of  German  silver 
wire  attached  to  these  binding-posts  are  united.  Then 
arrange  the  apparatus,  as  shown  in  Fig.  116.  The  lower 
part  of  this  figure  is  supposed  to  join  the  upper  part  at 
the  line  AB.  The  current  is  made  to  run  through  15 
turns  of  the  galvanoscope.  By  means  of  the  commutator 
the  current  can  be  easily  and  quickly  reversed  through 
the  galvanoscope.  Before  beginning  the  experiment,  the 
porous  cup  should  have  been  soaked  through  by  the  acid. 
This  can  best  be  done  by  pouring  the  acid  into  the  porous 
cup  a  few  minutes  before  the  cup  is  put  into  the  sulphate 
of  copper  solution.  As  the  rheostat  is  now  arranged,  the 
current  is  flowing  through  2m  of  German  silver  wire  (the 
resistance  of  the  short  piece  of  copper  wire  you  inserted 


ELECTRICAL    RESISTANCE. 


345 


between  the  two  binding-posts  may  be  neglected).  Read 
and  record  the  position  of  the  compass  needle,  which 
should  be  placed  at  the  center  of  the  shelf ;  the  coil 
itself,  before  the  current  is  allowed  to  flow  through, 
should  be  placed  nearly  in  the  magnetic  meridian.  Now, 
by  means  of  the  commutator,  reverse  the  current  through 


FIG.  116. 

the  galvanoscope,  and  again  record  the  reading.  Take  the 
average  of  the  two  deflections.  For  example,  suppose 
the  N-pointing  end  of  the  needle  to  have  come  to  rest  at 
42°  east  of  north  before  the  reversal  of  the  current,  and 
at  38°  west  of  north  after  the  reversal,  the  average,  or  40°, 
should  be  taken  as  the  true  deflection.  This  method  of 
reversal  and  averages  renders  it  unnecessary  to  place  the 
coil  accurately  in  the  magnetic  meridian.  (Why?) 

Now  remove  the  bit  of  copper  wire  which  you  inserted 
to  connect  the  two  pieces  of  German  silver  wire.     Con- 
nect these  same  two  German  silver  wires  by  means  of  ' 
the  English  binding-post,  which  should  be  placed  directly 


346 


EXPERIMENTAL    PHYSICS. 


beneath  the  90cm  mark  on  the  meter  stick.  The  current 
will  now  pass  through  180cm  of  the  wire. 

Read  the  galvanoscope,  which,  when  you  have  once 
begun  the  experiment,  you  must  not  disturb  till  the 
experiment  is  completed.  Reverse  the  current,  and  read 
again.  Shift  the  English  binding-post  to  a  position  under 
the  80cm  mark  of  the  meter  stick,  so  that  now  the  current 
will  flow  through  160cm  of  the  wire.  Read  the  galvan- 
oscope ;  reverse  the  current,  and  read  the  galvanoscope 
again.  By  shifting  the  English  binding-post,  make  the 
current  flow  in  turn  through  140cm,  120cm,  100cm,  80cm, 
and  60cm  of  the  wire.  For  every  change  in  position  of 
the  English  binding-post,  read  the  galvanoscope,  reverse 
the  current,  and  read  the  galvanoscope  again.  To  make 
sure  that  the  strength  of  the  cell  has  not  changed  during 
this  series  of  observations,  take  off  the  English  binding-post 
and  insert,  as  you  did  at  the  start,  the  bit  of  copper  wire, 
so  that  the  current  may  flow  through  the  2m  of  the  wire. 
Read  and  reverse  as  before.  If  the  strength  of  the  cell  is 
the  same  as  at  the  start,  the  average  deflection  just  obtained 
will  be  the  same  as  the  average  deflection  obtained  at  the 
beginning  of  the  experiment. 

A  convenient  form  in  which  to  enter  the  measurements 
in  your  note-book  is  the  following  : 


cin. 

200 

180 

160 

140 

120 

100 

80 

60 

200 

EAST 

o 

o 

o 

0 

o 

0 

o 

0 

0 

WEST 

AVERAGE 

ELECTKICAL  RESISTANCE.  347 

From  an  inspection  of  your  measurements,  can  you  see 
any  indication  of  what  change  in  the  resistance  of  a  wire 
an  alteration  in  its  length  makes ;  that  is,  does  a  long  wire 
offer  more  or  less  resistance  than  a  short  wire  of  the  same 
thickness  ? 

From  the  measurements  you  have  made,  the  exact  law 
stating  the  dependence  of  resistance  upon  the  length  of 
wire  cannot  be  inferred.  The  following  is  a  statement  of 
the  law  : 

The  resistance  of  a  wire  varies  directly  as  its  length. 

QUESTION.  If  there  are  two  wires  of  the  same  thickness  and  material, 
but  one  twice  as  long  as  the  other,  how  many  times  as  much  resistance 
will  the  longer  wire  have  than  the  shorter  ? 

Experiment  144.  To  find  what  influence  the  area  of 
cross-section  of  a  wire  has  upon  its  resistance  to  the  flow  of 
an  electric  current.1 

Apparatus.  The  same  as  in  the  preceding  experiment,  without 
the  English  binding-post. 

Directions.  Arrange  the  apparatus  as  in  the  preceding 
experiment,  only  shift  the  wires  leading  from  the  apparatus 
to  the  rheostat  from  the  lower  pair  of  binding-posts  to  the 
second  pair  above,  thus  putting  in  continuous  circuit  with 
the  galvanoscope  the  2m  of  No.  28  German  silver  wire. 
This  experiment  is  a  very  brief  one.  Simply  read  the 
galvanoscope,  reverse  the  current,  read  again,  and  record. 

Compare  the  average  deflection  thus  obtained  with  the 

1  If  this  experiment  is  not  performed  on  the  same  day  as  the  preceding 
experiment,  it  will  be  necessary  to  take  some  of  the  measurements  of  that 
experiment  over  again  to  make  sure  that  the  cell  has  undergone  no 
change  in  strength. 


348  EXPERIMENTAL   PHYSICS. 

deflections  obtained  with  various  lengths  of  No.  30  German 
silver  wire  in  the  last  experiment. 

What  length  of  No.  30  is  equivalent  in  resistance  to 
2m  of  No.  28  ? 

The  area  of  cross-section  of  No.  28  wire  is  about  1.46 
times  that  of  No.  ,30  ;  so  if  we  call  the  area  of  the  cross- 
section  of  No.  30,  1,  that  of  No.  28  will  be  1.46. 

Divide  the  length  of  No.  28  wire  (2m)  by  1.46. 

Divide  the  length  of  No.  30  wire  (of  equal  resistance) 
by  1. 

Are  the  two  quotients  equal  or  nearly  equal  ? 

What  relation  should  you  infer  exists  between  the  area 
of  cross-section  of  a  wire  and  its  resistance  ? 

157.  Divided  Circuit.  Suppose  a  branch  pipe  springs 
from  the  side  of  a  main  pipe  and  joins  the  main  pipe 
again  at  some  distance  from  the  starting-point,  the  branch 
thus  forming  a  loop  with  the  main  pipe.  If  water  flows 
along  the  main  pipe,  the  circuit  of  water  divides  when  it 
reaches  the  point  of  branching,  one  part  continuing  in  the 
main  pipe,  the  other  turning  aside  into  the  branch,  through 
which  it  flows  till  it  re-unites  with  the  current  in  the  main 
pipe.  Each  part  of  the  loop,  the  main  pipe  and  the  branch, 
offers  resistance  to  the  flow  of  water ;  but  the  combined 
resistance  of  both  parts  of  the  loop  is  less  than  that  offered 
by  either  alone,  so  that  by  both  branches  of  the  loop  taken 
together  less  resistance  is  offered  to  the  flow  than  by  an 
equal  length  of  the  main  pipe.  In  place  of  a  simple  loop 
of  two  branches  we  might  insert  one  or  more  additional 
branch  pipes,  and  thus*  have  a  loop  of  three  branches  or 
more.  The  current  would  then  divide  itself  among  all 


ELECTRICAL   RESISTANCE. 


349 


these  branches.  Just  as  a  current  of  water  divides  in 
branched  pipes,  so  a  current  of  electricity  divides  in  a 
branched  or  divided  circuit,  consisting  of  two  or  more 
wires  all  springing  from  the  same  point  and  all  coming 
together  again  at  another  point.  The  current  of  electricity 
on  entering  this  system  of  wires  at  one  of  these  two  meet- 
ing-points divides  itself  into  smaller  currents  among  the 
wires,  each  smaller  current  flowing  along  its  wire  till  it 
is  reunited  at  the  other  junction  with  the  other  smaller 
currents.  The  next  experiment  has  for  its  object  the  study 
of  resistance  in  a  divided  circuit. 

Experiment  145.  To  find  how  the  resistance  of  a 
divided  circuit  consisting  of  one  loop  compares  with  the 
resistance  of  half  the  loop. 

Apparatus.    The  same  as  in  the  last  experiment. 

Directions.     Connect  the  two  pieces  of  German  silver 
wire  that  have  already  been  used  on  the  rheostat  by  a  bit 
of  copper  wire  as  before.     Then  join 
this  united  wire  with  the  other  2m  of 
No.  30  German  silver  wire  in  "  mul- 
tiple arc "   circuit ;   that   is,  join   in 
divided  circuit  in  such  a  way  that 
part  of  the  current  will  go  through 
one  of  the  2m  pieces  of  wire,  the  other 
part  of  the  current  through 
"    the  other  2m  pieces  of  wire 

. as    shown    in    Fig.    117. 

Read  the  galvanoscope,  re- 
verse, and  read  the  galvanoscope  again ;  record. 

By  reference  to  the  record  of  Exp.  143,  what  length  of 


350  EXPERIMENTAL    PHYSICS. 

No.  30  German  silver  wire,  as  used  in  that  experiment, 
has  a  resistance  equal  to  that  of  the  two  2-meter  pieces  of 
No.  30  German  silver  wire  joined  in  multiple  arc  as  in  the 
present  experiment? 

What  part,  then,  of  the  resistance  of  a  single  2-meter 
piece  of  No.  30  wire  is  the  resistance  of  two  2-meter  pieces 
of  No.  30  wire  joined  in  multiple  arc  ? 

158.  The  Ohm.  In  order  to  measure  resistances,  a 
unit  of  resistance,  called  the  ohm,  has  been  established. 

Definition.  The  resistance  equal  to  that  offered  by  a 
column  of  mercury  of  uniform  cross-section,  at  0°,  106.3CI* 
long  and  of  mass  14-.^521&  ',  is  called  the  ohm. 


Copper  is  a  much  better  conductor  of  electricity  than 
mercury  is.  A  copper  wire  whose  area  of  cross-section  is 
I8qmm  would  have  to  be  about  45m  long  in  order  to  have  a 
resistance  of  one  ohm.  Among  metals  German  silver  has 
a  high  resistance,  and  its  resistance  varies  only  slightly 
with  the  temperature.  For  these  reasons  German  silver 
wire  is  employed  in  the  construction  of  resistance  coils, 
which  are  introduced  frequently  into  electrical  circuits  to 
modify  the  strength  of  the  current. 

Experiment  146.  To  find  what  length  of  Grerman  silver 
wire  is  equivalent  in  resistance  to  20m  of  copper  wire.1 

Apparatus.     The  same  as  in  the  preceding  experiment. 

Directions.     Put  the  20m  of  copper  wire,  No.  30,  into 
continuous  circuit  with  the  galvanoscope.     Read  the  gal- 
vanoscope,  reverse  the  circuit,  and  read  again  ;  record. 
1  See  note  at  bottom  of  page  347. 


ELECTRICAL   RESISTANCE.  351 

Compare  the  average  deflection  obtained  with  those 
obtained  in  Exp.  143,  and  so  find  the  length  of  German 
silver  wire  equivalent  to  that  of  the  copper.  Record. 

EXAMPLES. 

1.  If  a  wire  lm  long  has  a  resistance  of  1  ohm,  what  will  be  the 
resistance  of  a  wire  of  the  same  material  and  of  the  same  thickness  2m 
long  ?     10m  long  ?     0.5m  long  ? 

2.  If  a  wire  of  Isqmm  area  of  cross-section  has  a  resistance  of  1  ohm, 
what  will  be  the  resistance  of  a  wire  of  the  same  material  and  length,  but 
of  0.58<imm  cross-section  ?     28<i mm  area  of  cross-section  ?     108imm  area  of 
cross-section  ? 

3.  If  a  wire  lm  long  and  I8(i mm  area  of  cross-section  has  a  resistance  of 
1  ohm,  what  will  be  the  resistance  of  a  wire  of  the  same  material  2m  in 
length  and  2si mm  in  area  of  cross-section  ? 

4.  If  a  wire  2m  long  and  lmm  in  diameter  has  a  resistance  of  3  ohms, 
what  will  be  the  resistance  of  a  wire  of  the  same  material  4m  long  and 
2ram  in  diameter  ? 

Solution.  If  a  wire  2m  long  and  lmm  in  diameter  has  a  resistance  of 
3  ohms,  a  wire  lm  long  and  lmm  in  diameter  will  have  a  resistance  of 
1.5  ohms.  If  x  denotes  the  resistance  in  ohms  of  a  piece  of  wire  4m  long 

and  2mm  in  diameter,  -  will  denote  the  resistance  of  a  wire  lm  long  and 

2mm  m  diameter.  A  wire  2mm  in  diameter  has  four  times  the  area  of 
cross-section  of  a  wire  lmm  in  diameter,  since  the  areas  of  circles  are  to 
each  other  as  the  squares  of  their  diameters ;  consequently  a  wire  lm  long 

and  lmm  in  diameter  would  have  a  resistance  of  —  X  4  =  x.     But  the 

4 

resistance  of  a  wire  lm  long  and  lmm  in  diameter  has  previously  been 
found  to  be  1.5  ohms ;  hence  x=l.b. 

That  is,  the  resistance  of  the  wire  which  is  4m  long  and  2mm  in  diameter 
is  1.5  ohms. 

5.  A  wire  10m  in  length  and  lmm  in  radius  has  a  resistance  of  2  ohms  ; 
what  must  be  the  radius  of  another  wire  of  the  same  material  whose  length 
is  5m,  in  order  that  it  may  have  the  same  resistance  as  the  first  wire  ? 

6.  A  wire  of  length  V  and  diameter  d'  has  a  resistance  of  r  ohms; 
what  is  the  resistance  of  a  wire  of  the  same  material  of  length  I "  and 
diameter  d"  ? 


352  EXPERIMENTAL   PHYSICS. 

ELECTRO-MOTIVE    FORCE. 

159.  The  Volt.     The  term  electro-motive  force  is  one 
which  often  occurs  in  books  on  the  subject  of  electricity. 
The    term   may  best  be  explained  for  the   beginner  by 
analogy,  thus :  "  Just  as  in  the  water  pipes  a  difference  of 
level  produces  a  pressure,  and  the  pressure  produces  a  flow 
as  soon  as  the  tap  is  turned,  so  difference  of  electrical  level 
produces  electro-motive  force,  and  electro-motive  force  sets 
up  a  current  as  soon  as  a  circuit  is  completed  for  the 
current  to  flow  through."     The  unit  of  E.M.F.  (electro- 
motive force)  is  called  the  volt,  in  honor  of  Volta,  an 
Italian  physicist. 

The  E.M.F.  of  the  Daniell  cell  is  about  1.1  volts. 

It  has  been  proved  on  investigation  that  the  E.M.F.  of 
a  cell  depends  not  upon  the  size  of  the  plates,  but  upon 
the  materials  comprising  the  cell. 

160.  Ohm's  L.aw.     Ohm,  a  German  physicist,  discov- 
ered that  the  strength  of  a  current  of  electricity  is  equal 
to  the  E.M.F.  driving  the  current,  divided  by  the  resist- 
ance which  the.  current  encounters ;  that  is, 

,      .  E.M.F. 

strength  01  current  =  — r 

0  -../-kOT 


resistance 

For  the  sake  of  brevity  the  law  is  usually  stated  in  the 
following  form  : 


where  O  stands  for  strength  of  current,,  j&  for  E.M.F.,  and 
R  for  resistance. 

QUESTIONS.     What  is  the  name  of  the  unit  of  current  strength  ?     Of 
the  unit  of  E,M.F,  ?     Of  the  unit  of  resistance  ? 


BATTERY   RESISTANCE.  353 

If  there  is  a  circuit  in  which  the  E.M.F.  is  1  volt,  and  the  resistance 
1  ohm,  what  is  the  strength  of  the  current  ? 

If  a  battery  having  an  E.M.F.  of  5  volts  is  placed  in  a  circuit  of  which 
the  total  resistance  is  100  ohms,  what  will  be  the  strength  of  the  current  ? 


BATTERY   RESISTANCE. 

161.    Resistance   to  the  Current  in  the   Cell.      The 

liquids  in  a  cell  offer  to  the  flow  of  the  electric  current  a 
resistance  whose  magnitude  depends,  not  only  upon  the 
character  of  the  liquids,  but  also  upon  the  size  of  the 
plates  and  their  distance,  apart. 

In  writing  Ohm's  Law  in  the  literal  form,  it  is  customary 
to  denote  by  R  the  resistance  in  the  part  of  the  circuit 
that  lies  outside  the  battery,  and  by  r  the  resistance 
offered  by  the  cell  itself ;  so  we  have 

.Jf. 
'  + 

R  for  brevity  is  called  the  external  resistance;  r  is  called 
the  internal  resistance. 

Experiment  147.  To  find  whether  a  difference  in  size 
and  position  of  the  plates  of  a  cell  produces  a  variation  in  the 
strength  of  a  current. 

Apparatus.  Two  Daniell  cells  with  the  liquids  equally  deep  in 
both,  one  furnished  with  a  plate  of  zinc  and  a  plate  of  copper  of  the 
same  size  as  in  Exp.  140,  the  other  with  plates  10cm  long  and  0.5cm 
wide,  each  plate  having  a  wire  soldered  to  it  for  making  electrical 
connections  ;  a  galvanoscope  ;  a  rheostat ;  a  commutator. 

PART  1.     When  the  cell  with  large  plates  is  used. 

Directions.  Before  making  any  measurements,  see  that 
the  porous  cups  are  thoroughly  soaked  by  the  solutions. 


354  EXPERIMENTAL   PHYSICS. 

Join  the  cell  having  the  large  plates  to  the  commu- 
tator ;  also  join  the  5-turn  section  of  the  galvanoscope 
to  the  commutator.  By  this  arrangement  the  current 
through  the  galvanoscope  can  be  readily  reversed.  Read 
the  galvanoscope,  with  the  plates  as  far  apart  in  the  cell 
as  possible.  Then,  by  means  of  the  commutator,  reverse 
the  current,  and  read  the  galvanoscope  again.  Record  the 
readings,  and  find  their  average. 

PART  2.     When  the  cell  with  small  plates  is  used. 

Directions.  Now  disconnect  the  cell  from  the  galvan- 
oscope, and  put  the  cell  with  small  plates  into  the  circuit. 
Put  the  plates  as  far  apart  as  the  large  plates  of  the  other 
cell  were  placed,  read  the  galvanoscope,  reverse  the  cur- 
rent, and  read  the  galvanoscope  again.  Record  the  read- 
ings, and  find  their  average.  In  this  and  subsequent 
experiments,  whenever  you  are  directed  to  read  the  gal- 
vanoscope, bear  in  mind  that  the  readings  are  to  be  taken 
one  before  and  the  other  after  the  current  has  been 
reversed.  Put  the  plates  as  near  together  as  possible, 
and  read  again. 

After  an  inspection  of  your  record,  answer  the  following 
questions  : 

With  the  small  cell,  do  you  get  the  stronger  current 
when  the  plates  are  far  apart  or  when  they  are  close 
together  ? 

Do  you  get  a  stronger  current  with  the  cell  having 
large  plates  or  with  the  cell  having  small  plates  placed 
as  far  apart  as  those  of  the  large-plate  cell  are  ? 

NOTE.  When  the  plates  in  the  small-plate  cell  are  put  nearer  together, 
the  liquid  path,  which  the  current  in  its  passage  from  one  plate  to  the  other 


BATTERY    RESISTANCE.  355 

traverses,  is  shortened ;  consequently,  the  internal  resistance  of  the  cell 
is  diminished.  When  the  plates  of  two  cells,  as  in  the  experiment  just 
performed,  are  of  different  sizes,  but  the  length  of  the  liquid  conductor 
between  them  is  the  same,  the  cross-section  of  the  liquid  conductor  in 
the  cell  having  the  larger  plates  is  larger  than  that  of  the  other  cell ; 
hence,  the  internal  resistance  of  the  large-plate  cell  is  less  than  that  of 
the  small-plate  cell. 

In  the  experiment  just  performed  the  external  resistance  was  small. 
The  next  experiment  differs  only  in  this  respect,  that  the  external  resist- 
ance is  to  be  made  larger. 

Experiment  148.  To  find  whether  a  difference  in  size 
and  position  of  the  plates  of  a  cell  produces  the  same 
variation  in  the  strength  of  the  current  when  the  external 
resistance  is  large  as  it  does  when  this  resistance  is  small. 

Apparatus.  The  same  as  in  the  previous  experiment  together 
with  a  rheostat. 

Directions.  Put  the  narrow-plate  cell  into  circuit  with 
the  15  turns  of  the  galvanoscope,  and  2m  of  the  No.  30 
German  silver  wire  in  the  rheostat,  inserting  the  commu- 
tator in  order  to  reverse  the  current  through  the  galvan- 
oscope. With  this  arrangement  repeat  Part  2  of  the 
preceding  experiment. 

Then  disconnect  the  narrow-plate  cell,  and  put  in  its 
place  the  large-plate  cell.  Then  with  this  arrangement 
take  readings,  as  in  Part  1  of  the  preceding  experiment. 

Has  the  current,  in  this  experiment  with  the  added 
external  resistance,  shown  more  or  less  fluctuation  for 
change  in  size  and  position  of  the  plates  than  when,  as 
in  the  preceding  experiment,  the  external  resistance  was 
smaller  ? 

Ohm's  Law  may  help  you  in  understanding  the  results 
you  have  obtained. 


356  EXPERIMENTAL   PHYSICS. 

By  inspection  of  the  literal  form  of  Ohm's  Law  it  will 
be  seen,  after  a  little  consideration,  that  when  the  external 
resistance,  R,  is  small,  a  variation  in  the  internal  resist- 
ance, r,  will  sensibly  affect  the  value  of  (7;  on  the  other 
hand,  when  R  is  large  and  r  small,  a  variation  in  r  will 
produce  no  sensible  change  in  the  value  of  C. 

To  make  this  clearer,  let  us  take  a  numerical  example. 

(1)  When  the  external  resistance,  R,  is  small. 
Let  R  =  \,  r—2. 

c=fT2  =  f- 

Change  the  value  of  r  from  2  to  3. 

^iff-f 

Hence,  in  this  case,  by  increasing  r  by  1,  the  value  of 

•pi        -pi 

the  current,  (7,  is  diminished  from  —  to  —  ,  or,  expressed 

o         4 

in  decimal  form,  from  0.33  E  to  0.25  E. 

(2)  When  the  external  resistance,  R,  is  large. 
Let  12  =  100,  r=2. 

° 


Change  the  value  of  r  from  2  to  3. 

The"  °=Io5T8  =  iS- 

Hence,  by  increasing  r  by  1,  the  value  of  the  current,  (7, 
•pi          -pi 

is  diminished  from  —  —  to  —  —  ,  or,  expressed  in  decimal 
10.2        lOo 

form,  from  0.0098  E  to  0.0097  E, 


ARRANGEMENT    OF    CELLS.  357 

ARRANGEMENT    OF    CELLS. 

Experiment  149.  To  find,  provided  the  external  resist- 
ance is  small,  which  is  the  stronger,  the  current  from  two 
cells  joined  abreast  or  from  two  cells  joined  in  series. 

Apparatus.  Two  Daniell  cells  provided  with  full-sized  plates  (such 
plates  as  used  in  Exp.  147,  Part  1)  ;  a  galvanoscope  ;  a  commutator. 

PART  1.     When  the  cells  are  joined  abreast. 

Directions.  Join,  so  as  to  make  good  metallic  contact, 
the  ends  of  the  wires  leading  from  the  zinc  plates  of  the 
two  cells  ;  also  join  the  wires  leading  from  the  coppers  of 
the  two  cells.  Put  the  cells  thus  joined  into  circuit  with 
the  5-turn  section  of  the  galvanoscope.  Cells  joined  in 
this  way  are  said  to  be  joined  abreast.  Insert  a  commu- 
tator into  the  circuit  for  reversing  the  current  through 
the  galvanoscope.  Read  the  galvanoscope,  and  record  the 
deflections. 

PART  2.     When  the  cells  are  joined  in  series. 

Directions.  Now  disconnect  the  cells,  and  join  the 
wire  from  the  zinc  of  one  cell  to  the  copper  of  the  other 
cell.  Put  the  battery  into  circuit  with  the  5-turn  section 
of  the  galvanoscope ;  insert  the  commutator  to  change  the 
current  through  the  galvanoscope.  When  arranged  in 
this  way,  the  cells  are  said  to  be  joined  in  series. 

Read  the  galvanoscope,  and  record  the  deflections. 

With  which  arrangement  of  cells  did  you  obtain  the 
stronger  current? 

Experiment  15O.  To  find,  provided  the  external  resist- 
ance is  large,  which  is  the  stronger,  the  current  from  two 
cells  joined  abreast  or  from  two  cells  joined  in  series* 


358  EXPERIMENTAL    PHYSICS. 

Apparatus.  The  same  as  in  the  last  experiment  together  with  a 
rheostat. 

PART  1.     When  the  cells  are  joined  abreast. 

Directions.  As  in  Part  1  of  the  last  experiment,  join 
the  cells  abreast,  and  then  put  them  in  circuit  with  the 
15  coils  of  the  galvanoscope  and  the  2m  piece  of  No.  30 
German  silver  wire  in  the  rheostat ;  insert  the  commutator 
to  change  the  current  through  the  galvanoscope.  Read 
the  galvanoscope ;  record  its  deflections. 

PART  2.     When  the  cells  are  joined  in  series. 

Directions.  Now  join  the  cells  in  series,  and  put  them 
in  circuit  with  the  15  coils  of  the  galvanoscope,  2m  No.  30 
German  silver  wire,  and  commutator.  Read  the  galvano- 
scope ;  record  its  deflections. 

With  which  arrangement  of  cells  did  you  get  the 
stronger  current? 

162.    Arrangement  of  Cells  Abreast  and  in  Series. 

From  your  experiments  you  have  been  led  to  the  con- 
clusion that  when  the  external  resistance  is  small,  the 
internal  resistance  must  be  small ;  and,  on  the  other  hand, 
when  the  external  resistance  is  large,  the  internal  resistance 
must  be  large. 

Careful  experiments  have  shown  that  the  E.M.F.  of  a 
battery  depends  upon  the  number  of  cells,  joined  in  series  ; 
a  battery  of  two  cells,  joined  in  series,  has  an  E.M.F. 
equal  to  the  sum  of  the  E.M.F.  of  each ;  if  the  E.M.F.  is 
the  same  for  each  cell,  then  of  course  the  E.M.F.  of  the 
battery  is  twice  that  of  one  of  the  cells  ;  the  E.M.F.  of  a 
battery  consisting  of  five  cells  of  the  same  strength,  joined 
in  series,  is  five  times  that  of  a  single  cell ;  finally,  the 


ARRANGEMENT    OF    CELLS.  359 

E.M.F.  of  a  battery  composed  of  n  cells  of  equal  strength, 
joined  in  series,  is  n  times  that  of  a  single  cell. 

It  has  also  been  shown  that  a  battery  of  two  cells  of 
equal  strength,  joined  abreast,  has  the  same  E.M.F.  as  a 
single  cell ;  a  battery  of  five  cells  of  equal  strength,  joined 
abreast,  has  the  same  E.M.F.  as  a  single  cell ;  and,  finally, 
a  battery  consisting  of  n  cells  of  equal  strength,  joined 
abreast,  has  the  same  E.M.F.  as  a  single  cell. 

Accurate  experiments  have  also  shown  that  the  internal 
resistance  of  a  battery  of  ten  cells  joined  in  series  is  equal 
to  the  sum  of  the  internal  resistances  of  the  cells ;  or  if  the 
cells  are  of  equal  internal  resistance,  the  internal  resist- 
ance of  a  battery  composed  of  two  cells  joined  in  series  is 
twice  that  of  one  cell.  In  fact,  if  cells  of  equal  resistance 
are  joined  in  series,  the  internal  resistance  of  the  battery 
thus  formed  is  equal  to  the  resistance  of  one  cell  multi- 
plied by  the  number  of  cells. 

If  two  cells  of  equal  internal  resistance  be  joined  abreast, 
the  internal  resistance  of  the  battery  thus  formed  would 
be  one-half  the  resistance  of  a  single  cell.  If  n  cells  of 
equal  internal  resistance  be  joined  abreast,  the  internal 

resistance  of  the  group  would  be  -  of  the  resistance  of  a 

n 

single  cell. 

Whenever  you  desire  to  group  a  given  number  of  cells 
in  order  to  form  a  battery  that  will  give  the  maximum, 
or  strongest,  current  through  a  known  external  resistance, 
you  should  be  guided  by  the  following 

Rule.  Join  the  cells  in  such  a  way  as  to  make  the  inter- 
nal resistance  of  a  battery  equal,  as  nearly  as  possible,  to  the 
external  resistance. 


360 


EXPERIMENTAL    PHYSICS. 


We  shall  illustrate  this  rule  by  the  following  example  : 

There  are  12  cells,  each  of  E.M.F.  1  volt  and  internal 

resistance  i  ohm,  and  there   is  a  wire  the  resistance  of 

which  is  2  ohms.     How  must  the  cells  be  arranged  in 

order  to  yield  the  maximum  current  through  the  wire  ? 

Let  us  arrange  the  cells  in  various  ways  and  compute 
the  strength  of  the  current. 

(1)    All  the  cells  in  series  (Fig.  118). 


FIG.  118. 


By  Ohm's  Law  we  can  find  the  strength  of  the  current 
with  this  arrangement  : 

E  12  X  1  12 

C=  -      -  =  --  —  -  =  —  =  1  .5  amperes. 
E      r       2       12x  8 


FIG.  119. 


ARRANGEMENT    OF   CELLS. 


361 


(2)  2  cells  abreast  and  6  in  series  (Fig.  11-9). 

0= ^-^ =  —  =  1 .71  amperes. 

2+1x6x1        7 

(3)  3  cells  abreast  and  4  in  series  (Fig.  120). 

R 


R 


H 


FIG.  120. 


FIG.  121. 


0  = 


4X1 


12 


=  — -  =  1.5  amperes. 


2+1X4X \ 
(4)    4  cells  abreast  and  3  in  series  (Fig.  121). 

0=±-  -  =  ?i  =  1.26  amperes. 

2          X3x          19 


362 


EXPERIMENTAL    PHYSICS. 


(5)    6  cells  abreast  and  2  in  series  (Fig.  122). 

C=-  —  =  if  =r  0.95  ampere. 

2  +  J  X  2  X  \       13 

(6)    All  the  cells  abreast. 
c_  I  _24_Q19 

We  have  grouped  the  cells  in  many  differ- 
ent ways,  and  find  that  the  strongest  current 
is  obtained  in  the  second  arrangement,  when 
the  internal  resistance  and  the  external  re- 
sistance are  as  nearly  equal  as  possible.  It 
can  be  proved  by  algebra  that  the  strongest 
current  is  obtained  when  the  external  resist- 
ance and  the  internal  resistance  are  equal ; 
but  such  a  proof  is  beyond  the  scope  of 
this  book. 

EXAMPLES. 

1.  How  should  10   cells,  each  having  an  internal 
resistance  of  1  ohm,  be  arranged  in  order  to  send  the 
strongest  current  possible  through  a  resistance  of  12 
ohms  ? 

2.  How  should-  12  cells,  each  having  an  internal 
resistance  of  £  ohm,  be  arranged  in  order  to  send  the 
strongest  current  through  a  resistance  of  1  ohm  ? 

Solution.  If  x  denotes  the  number  of  cells  in  series, 
then  12  -j-  x  will  denote  the  number  of  cells  abreast, 

and  the  internal  resistance  of  the  battery  will  be  — —t — ; 

i  —  ~T~  & 

x  must  have  such  a  value  as  to  make  this  resistance 
FIG.  122.  e<lual  !»  hence  ^ 

12 


—  tn 

R 

nnn 

l-l 

r^— 

1 

H 
i 

1 

1 

i 

i 

1 
_i 

i 

1 
_i 

i 

n 

J 

i 
i 

=  12, 
=  16, 


ELECTRO-MAGNETISM.  363 

That  is,  the  battery  must  be  arranged  with  four  cells  in  series  and  con- 
sequently with  three  cells  abreast. 

3.  Four  cells,  each  of  E.M.F.  1  volt  and  internal  resistance  2  ohms, 
are  to  be  arranged  to  send  the  strongest  current  possible  through  an 
external  resistance  of  2  ohms ;  what  must  the  arrangement  be  ? 

4.  There  are  two  cells,  each  having  a  resistance  of  2  ohms ;  how  should 
the  cells  be  arranged  in  order  to  get  the  strongest  current  when  the  ex- 
ternal resistance  is  1  ohm  ?     2  ohms  ?    4  ohms  ? 

5.  How  should  20  Daniell  cells,  each  with  a  resistance  of  1  ohm,  be 
grouped  in  order  to  send  the  strongest  current  through  a  resistance  of 
0.9  ohm? 

ELECTRO-MAGNETISM. 

163.  The  Electro  -  Magnet ;  Telegraph  Key  and 
Sounder.  The  object  of  the  next  experiment  will  be  to 
bring  out  the  properties  of  the  electro-magnet,  and  also 
to  show  how  the  electro-magnet  can  be  used  to  reproduce 
signals  made  at  a  long  distance  from  the  electro-magnet. 

Experiment  151.  To  find  what  influence  a  current  of 
electricity  has  upon  a  piece  of  iron,  when  flowing  through  a 
wire  wound  round  the  iron. 

Apparatus.  A  Daniell  cell ;  a  cylinder  of  soft  iron  about  7cm  long 
and  0.7cm  in  diameter ;  insulated  copper  wire,  No.  30  B.  &  S. ; 
a  piece  of  pine  wood  about  20cm  square  ;  sheet  spring  brass  about 
0.5mm  thick ;  a  disc  of  soft  iron  0.3cm  thick  and  0.7cm  in  diameter. 

PART  1.     The  electro-magnet. 

Directions.  Wind  the  wire  upon  the  cylinder  of  soft 
iron,  just  as  thread  is  wound  upon  a  spool,  making  one  or 
two  layers. 

When  the  ends  of  the  wire  are  joined  to  the  cell,  and 
the  disc  of  soft  iron  is  brought  near  one  end  of  the  iron 
cylinder,  what  is  the  result  ? 


364  EXPERIMENTAL   PHYSICS. 

When  the  circuit  is  broken,  that  is,  when  one  end  of 
the  wire  is  disconnected  from  the  cell,  what  happens  to 
the  iron  disc? 

What  is  an  electro-magnet? 

PART  2.  The  electro-magnet  used  in  the  construction 
of  a  telegraphic  key  and  sounder. 

Directions.  Cut  from  the  sheet  brass  a  strip  about 
10cm  long  and  about  0.7cm  wide.  Solder  the  iron  disc  flat- 
wise to  the  side  of  the  brass  strip  near  one  end  (see  note 
on  page  139);  to  the  other  end  solder  a  flat-headed  screw, 
so  that  the  length  of  the  screw  shall  be  at  right  angles  to 
the  length  of  the  strip,  and  one  edge  of  the  strip  shall 
touch  the  under  side  of  the  head  of  the  screw.  Insert  the 
screw  into  the  board  at  a  point  on  a  diagonal  about  6cm 
from  the  corner,  turning  the  screw  till  the  strip  is  parallel 
to  the  side  of  the  board  and  the  center  of  the  disc  is  about 
on  a  line  with  the  center  of  the  electro-magnet  which  you 
have  made,  when  the  electro-magnet  is  laid  upon  its  side 
on  the  board.  Fasten  the  electro-magnet  in  place  by  a  bit 
of  leather  laid  over  the  magnet  and  tacked  to  the  board  at 
each  end.  Cut  another  strip  from  the  brass.  This  strip 
should  be  about  12cm  long  and  1.5cm  wide,  and  should  be 
bent  at  right  angles  to  its  length  at  a  distance  of  about 
3cm  from  one  end,  and  again  at  right  angles,  but  in  the 
opposite  direction,  at  a  distance  of  lcm  from  the  same  end. 
Through  the  center  of  this  bent  end,  which  is  lcm  long,  a 
hole  should  be  made.  A  screw  should  be  inserted  through 
this  hole  into  the  board.  Some  of  the  insulating  material 
should  be  removed  from  one  end  of  the  magnet  wire. 
This  end  should  be  wound  round  the  screw,  passing 


GALVANOMETERS.  365 

through  the  brass,  two  or  three  times,  and  then  the  screw 
should  be  "set  up"  till  everything  is  fast.  A  screw 
should  be  inserted  into  the  board,  under  the  free  end  of 
the  brass  strip,  to  such  a  distance  as  to  allow  a  space  of 
about  lcm  between  the  head  of  this  screw  and  the  under 
side  of  the  brass  strip.  When  a  wire  from  the  cell  is 
joined  to  this  screw,  and  the  other  end  of  the  magnet  wire, 
from  which  the  insulating  material  has  been  removed,  is 
also  connected  to  the  cell,  the  apparatus  is  completed. 
When  the  brass  strip,  called  the  key,  is  pressed  down  till 
it  touches  the  screw,  the  circuit  through  the  electro- 
magnet is  completed,  and  the  little  disc  of  iron,  called  the 
armature,  fastened  to  the  end  of  the  horizontal  strip,  is 
attracted  to  the  electro-magnet.  The  electro-magnet  and 
the  armature  are  together  called  a  sounder.  Before  the 
sounder  will  work  in  a  satisfactory  manner,  the  armature 
may  have  to  be  adjusted  by  turning  the  screw  so  as  to 
bring  the  armature  nearer  the  magnet  or  to  carry  it  far- 
ther away.  When  the  suitable  adjustments  have  been 
made,  the  armature  will  strike  the  electro-magnet  with 
a  sharp  click  whenever  the  key  is  depressed. 

Join  your  instrument  to  that  made  by  some  other 
student,  and  try  to  transmit  signals  from  one  instrument 
to  the  other. 

State  how  a  method  might  be  devised  for  sending 
signals  from  one  house  to  another,  by  means  of  an  instru- 
ment similar  to  that  which  you  have  made. 

GALVANOMETERS. 

164.  The  Tangent  Galvanometer;  the  Astatic  Gal- 
vanometer. The  galvanoscope  which  we  have  used  in 


366  EXPERIMENTAL    PHYSICS. 

testing  the  presence  of  a  current  of  electricity  might 
also  be  used  to  measure  the  strength  of  the  current,  the 
strength  of  the  current  being  proportional,  not  to  the 
angle  through  which  the  needle  is  deflected,  but  to  the  tan- 
gent1 of  the  angle  through  which  the  needle  is  deflected. 
In  the  tangent  galvanometer,  the  current  passing  through 
the  coil  tends  to  deflect  the  needle, 
while  the  earth's  magnetic  force  re- 
sists this  tendency;  consequently, 
whenever  a  very  weak  current  flows 
through  the  coil,  there  is  little  or  no 
deflection  of  the  needle  to  be  observed. 
To  indicate  the  presence  of  a  weak 
current,  we  must  use  a  more  delicate 
instrument,  called  an  astatic  galvan- 
ometer. 

This  instrument,2  as  shown  in  Fig. 
123,  consists  of  a  flat  coil  of  insulated 

FIG.  123. 

wire,  placed  m  a  horizontal  position, 

over  which  is  laid  a  circular  card  graduated  in  degrees. 
From  an  upright  support  is  hung,  by  a  delicate  fiber,  a 
little  contrivance,  resembling  the  letter  H  turned  on  its  side 
with  the  cross  line  carried  beyond  one  side,  as  shown  in 
Fig.  124.  This  H-shaped  contrivance  is  made  of  alumi- 
num, or  some  other  light  and  rigid  substance.  On  each 
of  the  sides  of  the  H  is  fastened  a  magnet,  indicated  by 
the  heavy  black  lines  in  the  figure.  -  These  magnets  are 

1  If  from  any  point  in  one  side  of  an  angle  a  perpendicular  is  dropped 
to  the  other  side,  the  tangent  of  the  angle  is  equal  to  the  ratio  of  the 
perpendicular  and  that  part  of  the  side  included  between  the  vertex  of 
the  angle  and  the  foot  of  the  perpendicular. 
-  2  Devised  by  Dr.  E.  H.  Hall. 


GALVANOMETERS.  367 

turned  in  opposite  directions,  so  that  the  N-pointing  pole 
of  the  upper  magnet  is  directly  over  the  S-pointing  pole 
of  the  lower  magnet,  and  the  magnets  are  of  nearly  equal 
strength.  Consequently,  the  earth's  action  upon  this 
combination  of  two  magnets  has  but  little  effect  in 
making  it  take  a  definite  direction.  In  Fig.  124,  E  repre- 
sents the  fiber  which 
supports  the  mag- 
nets, D  represents 
the  graduated  scale 
over  which  the  side 
of  the  H  carrying 
the  upper  magnet 
moves,  C  represents 
the  coil  through 

,  .    ,        ,,  FIG.  124. 

which    the   current 

of  electricity  flows.  The  arrows  denote  the  direction  in 
which  the  current  is  supposed  to  be  flowing.  If  the 
N-pointing  pole  of  the  lower  magnet  is  pointing  to  the 
right,  the  action  of  the  current  upon  this  magnet  will 
be  to  turn  its  N-pointing  pole  away  from  the  observer, 
in  consequence  of  the  magnetic  action  of  currents  on 
magnets  which  you  have  already  examined  in  Exp.  137. 
The  effect  of  the  current,  in  the  upper  half  of  the  coil,  on 
the  upper  magnet  will  be  to  turn  it  in  the  direction  in 
which  the  lower  magnet  is  turned ;  the  effect  of  the  lower 
half  of  the  coil  will  be  to  turn  the  upper  magnet  in  the  op- 
posite direction.  This  effect,  however,  is  slight,  because 
the  lower  half  of  the  coil  is  so  far  from  the  magnet.  The 
current  acts  strongly  upon  the  magnets  to  turn  them  in  the 
same  direction,  while  the  earth's  action  upon  them  is  very 


368  EXPERIMENTAL    PHYSICS. 

slight.  The  H-shaped  piece  to  which  the  magnets  are 
fastened  is  very  easy  to  move,  since  the  fiber  offers  little 
resistance  to  twisting.  Hence,  this  arrangement  of  the 
magnets  and  the  coil  gives  an  excellent  means  of  detect- 
ing the  presence  of  feeble  currents. 

On  the  base  of  the  support  (Fig.  123)  on  which  the 
coil  rests  are  leveling  screws.  By  turning  these  screws, 
the  instrument  can  be  adjusted  so  that  the  H-shaped  piece 
will  hang  freely  without  touching  either  the  sides  of  the 
slot  in  the  cardboard  scale  or  the  coil  itself.  At  the  upper 
end  of  the  support  to  which  the  end  of  the  fiber  is  attached 
is  a  little  screw.  By  loosening  this  screw,  the  magnets  can 
be  raised  or  lowered,  thus  bringing  the  upper  side  of  the 
H-shaped  piece  the  proper  distance  from  the  scale.  A  glass 
shade  covers  everything  in  order  to  keep  out  currents  of 
air,  which  would  set  the  magnets  swinging.  Two  binding- 
posts  in  front  serve  to  connect  the  coil  with  the  wires 
carrying  the  current  of  electricity. 

MEASUREMENT    OF    RESISTANCE. 

165.    Method  of  Substitution ;    Bridge  Method.     In 

our  experiments  on  electrical  resistance,  Arts.  151,  152, 
we  made  use  of  the  method  of  substitution.  We  allowed  a 
current  of  electricity  to  flow  through  a  wire,  and  noted 
the  deflection  of  the  galvanoscope  needle ;  then  we  found 
another  wire  which  would  offer  the  same  resistance  to 
the  current  which  the  first  wire  offered,  that  is,  when  a 
current  of  the  same  strength  flowed  through  the  second 
wire  as  through  the  first,  the  needle  would  be  deflected 
equally.  If  we  had  actually  known  the  resistance  of  the 


MEASUREMENT   OF   RESISTANCE.  369 

second  wire  in  ohms,  we  should,  also  know  the  resist- 
ance of  the  first  wire.  To  measure  resistances  by  this 
method,  then,  we  should  have  to  note  the  deflection 
produced  in  the  needle  of  the  galvanoscope  when  a 
current  was  flowing  through  the  wire  the  resistance 
of  which  we  wish  to  get;  then  we  should  have  to 
substitute,  for  the  wire  of  unknown  resistance,  wires  of 
known  resistance  till  the  current  gave  the  same  deflection 
as  before.  This  method  is  not  as  good  as  the  bridge 
method,  in  which  use  is  made  of  an  instrument  called 
Wheatstone's  bridge. 

Before  describing  this  instrument,  we  must  examine 
the  meaning  of  the  term  equipotential  points. 

166.   Electrical  Potential;  Equipotential  Points.    In 

order  that  water  may  flow  from  one  point  to  another, 
there  must  be  a  difference  of  level.  In  order  that  elec- 
tricity may  flow,  there  must  be  a  difference  of  potential,  or 
electrical  level.  Whenever  two  points  have  the  same  level, 
water  cannot  flow  from  one  to  the  other  ;  whenever  two 
points  have  the  same  potential,  a  current  of  electricity 
cannot  flow  from  one  to  the  other  through  a  wire  joining 
them.  Two  points  which  have  the  same  potential  are 
called  equipotential  points.  The  following  experiment  will 
make  clearer  the  term  equipotential  points. 

Experiment  152.  To  find  the  relation  between  the 
length*  of  the  segments  of  a  wire  divided  by  a  point  and 
the  resistances  of  the  segments  of  another  wire  divided  by  a 
point  which  has  the  same  potential  as  the  first. 

Apparatus.  A  frame  on  which  is  stretched  a  German  silver  wire ; 
a  Daniell  cell;  an  astatic  galvanometer;  a  piece  of  copper  wire  a 


370  EXPERIMENTAL   PHYSICS. 

little  more  than  100cm  long  ;    insulated  copper  wires  for  making 
connections. 

Directions.  Fasten  one  end  of  the  copper  wire  and 
also  the  end  of  one  wire  from  the  cell  in  one  of  the  front 
binding-posts  in  the  frame  (Fig.  125).  Draw  the  copper 
wire  straight,  and  fasten  it  in  the  other  binding-post 
together  with  the  end  of  the  other  wire  from  the  cell. 
The  current  on  leaving  the  wire  from  the  cell  enters  the 
brass  strip  to  which  the  two  wires  are  attached,  where  it 
divides,  one  part  flowing  along  the  copper  wire,  the  other 


FIG.  125. 

part  along  the  German  silver  wire,  as  shown  by  the  arrows. 
These  currents  unite  when  they  reach  the  other  brass 
strip  to  which  the  wires  are  attached,  and  the  united 
currents  return  to  the  cell.  Connect  by  a  thin  wire  some 
point,  as  P1 ,  in  the  copper  wire  with  the  galvanometer, 
and  touch  the  wire  leading  from  the  other  binding-post  of 
the  galvanometer  to  the  German  silver  wire  at  various 
points  till  a  point  is  found  which  has  the  same  potential 
as  the  point  P',  so  that  no  current  flows  through  the  gal- 
vanometer. Call  this  point  P.  Measure  and  record  the 
lengths,  a  and  5,  c  and  d,  of  the  segments  of  the  two 
wires.  Then  change  the  position  of  Pr  and  find  the 
corresponding  position  of  P.  Record  the  measurements 
as  before.  Again  change  the  position  of  Pr;  make  measure- 
ments and  record* 


MEASUREMENT    OF    RESISTANCE.  371 

In  every  case  which  you  have  tried,  is  the  following 
proportion  true?  a  :  b  =  c  :  d. 

If  you  denote  the  resistances  of  the  segments,  a,  6,  e, 
and  c?,  by  A,  B,  C,  and  D,  respectively,  knowing  that  the 
resistance  of  a  wire  is  proportional  to  its  length,  are  the 
following  proportions  true  ? 

a  :  b  =  A  :  B, 
c:  d  =  C:  D. 
Is  the  following  proportion  true  ? 


C       a 
°r       = 


167.  Theory  of  Wheatstone's  Bridge.  Fig.  126  rep- 
resents a  Wheatstone's  bridge  in  the  form  of  a  diagram. 
The  horizontal  line  represents  a  wire  of  German  silver; 
the  curved  line  represents  another 
conductor  ;  the  wavy  lines  repre- 
sent the  wires  which  connect  the 
bridge  to  the  cell;  the  arrows 
represent  the  direction  of  the  cur- 
rent in  each  conductor  ;  Cr  is  the 
galvanometer  connected  by  wires 

to  the  equipotential  points  R  and  S.  The  point  S  has 
been  found  by  sliding  the  end  of  the  wire  joined  to  the 
galvanometer  along  the  German  silver  wire  till  no  current 
is  indicated  by  the  galvanometer.  From  the  results  of  the 
preceding  experiment  we  know  that 
r  :  x  =  a  :  6, 

x       b  b 

or     -  =  -•     .-.  x=  -  X  r. 
r       a  a 


372 


EXPERIMENTAL   PHYSICS. 


Experiment  153.      To  find,  by  the  bridge  method,  the 
resistance  of  a  piece  of  wire. 

Apparatus.     A  Wheatstone's  bridge  (Fig.  127)  ;  an  astatic  gal- 
vanometer ;  a  Daniell  cell ;  a  box  of  resistance  coils,  that  is,  coils  of 


FIG.  127. 

wire  of  known  resistance  which  can  readily  be  put  in  circuit ;  a  piece 
of  insulated  copper  wire,  No.  30  B.  &  S.,  200cm  or  300cm  long. 

Directions.  By  means  of  short,  thick,  copper  wires, 
whose  resistance  may  be  neglected,  join  the  resistance  box 
to  the  binding-posts  on  each  side  of  the  left-hand  gap  in 
the  brass  strip  which  nearly  surrounds  three  sides  of  the 
instrument,  as  shown  in  Fig.  127.  Join  the  resistance  to 
be  measured  to  the  binding-posts  on  either  side  of  the 
right-hand  gap.  Connect  one  wire  from  the  galvanometer 
to  the  binding-post  at  R,  and  the  other  wire  to  the  bind- 
ing-post on  the  piece  which  slides  along  the  scale  over 
which  the  German  silver  wire  is  stretched.  Connect  the 
cell  to  the  binding-posts  as  shown  in  the  figure.  When 


MEASUREMENT    OF    RESISTANCE.  373 

everything  is  ready,  touch  the  sliding  part  to  the  German 
silver  wire  and  quickly  remove  it,  noting  in  which  direc- 
tion the  vane  of  the  galvanometer  moves.  Then,  when 
the  vane  has  settled  somewhat,  touch  the  sliding  part 
again  to  the  German  silver  wire,  but  at  a  different  point, 
and  note  the  direction  in  which  the  vane  is  deflected. 
The  object  at  first  is  to  get  two  positions  for  the  sliding 
part  which  will  deflect  the  vane  in  opposite  directions. 
The  point  on  the  German  silver  wire  equipotential  to  R 
lies  somewhere  between  these  two  positions,  and  can  now 
be  readily  found.  If  the  point  S  thus  found  should 
happen  to  be  near  the  end  of  the  German  silver  wire, 
change  the  resistance  r,  by  adding  resistance  or  diminish- 
ing it,  till  8  is  at  least  20cm  from  the  end  of  the  wire. 

When  S  has  been  found  so  that  no  current  flows 
through  the  galvanometer,  record  the  length  of  a  and 
of  5;  also  record  the  resistance  r.  Compute  the  resist- 
ance x. 

TEMPERATURE   AND    RESISTANCE. 

168.  Temperature  Coefficient  of  Resistance.  When- 
ever a  copper  wire  is  heated,  its  resistance  increases.  In 
fact,  the  resistance  of  all  metals  increases  with  an  increase 
of  temperature.  The  object  of  the  following  experiment 
is  to  measure  the  resistance  of  a  copper  wire  at  0°,  and 
also  at  100°,  and  then  to  determine  what  is  known  as  the 
temperature  coefficient  of  resistance  for  copper. 

Experiment  154.  To  find  by  what  part  of  its  resistance 
at  0°  a  copper  wire  increases  in  resistance  for  a  rise  in 
temperature  of  1°. 


374  EXPERIMENTAL   PHYSICS. 

Apparatus.  In  addition  to  that  of  Exp.  153,  a  jar  of  ice-water 
with  many  pieces  of  floating  ice ;  a  copper  boiler  ;  a  Bunsen  burner  ; 
a  thermometer  ;  a  glass  tube  of  rather  large  diameter. 

Directions.  Wind  the  wire  rather  openly  round  the 
glass  tube,  and  put  the  tube  thus  wound  with  the  wire 
into  the  jar  of  ice-water.  Connect  the  ends  of  the  coil  to 
the  bridge  by  short,  thick,  copper  wires,  in  the  place  in 
which  the  resistance  x  (Fig.  127)  occupied  in  Exp.  153. 
Arrange  the  other  parts  of  the  apparatus  as  you  did  in 
Exp.  153,  and  find  the  resistance  of  the  copper  wire, 
after  thoroughly  stirring  the  ice  and  water  with  the  ther- 
mometer. Transfer  the  coil  of  wire  from  the  ice-water 
to  the  copper  boiler  partly  filled  with  water,  and  heat  this 
water  to  boiling.  Then  find  the  resistance  again  of  the 
wire. 

From  the  results  which  you  have  obtained,  answer  the 
following  questions : 

(1)  What  is  the  resistance  of  the  wire  at  0°  ? 

(2)  What  is  the  resistance  of  the  wire  at  100°  ? 

(3)  What  is  the  increase  in  the  resistance  of  the  wire 
for  a  rise  in  temperature  of  100°  ? 

(4)  What  is  the  average  increase  in  the  resistance  of 
the  wire  for  a  rise  in  temperature  of  1°? 

(5)  What  part  of  the  resistance  at  0°  is  the  increase  in 
resistance  for  1°? 

Definition.  The  temperature  coefficient  of  a  conductor  is 
a  number  which  tells  by  what  part  of  itself  the  resistance  at 
0°  has  increased  for  a  rise  in  temperature  of  1°. 


I JST  D  E  X 


Absolute  temperatures,  94  ;  units, 
300 ;  zero,  94. 

Acceleration,  289. 

Air,  21 ;  specific  gravity  of,  39. 

Air  thermometer,  93. 

Algebraic  sum,  261. 

Amalgamating  zinc,  337. 

Ampere,  the,  341. 

Amplitude,  158. 

Angle  of  incidence,  196;  of  fric- 
tion, 279;  of  reflection,  196; 
of  refraction,  214;  of  repose, 
279 ;  tangent  of  an,  366. 

Apparatus,  manufacturers  of,  v. 

Arrangement  of  cells  abreast,  357  ; 
in  series,  358 ;  rule  for,  359. 

Astatic  galvanometer,  366. 

Atmosphere,  21 ;  pressure  of,  30. 

Axis  of  abscissae,  60 ;  of  ordinates, 
60  ;  principal,  220 ;  secondary, 
221. 

Balance,  corrections  of,  133 ;    zero 

error  of,  5. 
Barometer,  33. 

Battery,. 326 ;  resistance  of  a,  353. 
Beats,  175. 
Boiling,  123. 

Boiling-point  of  water,  79. 
Boyle,  Robert,  41. 
Boyle's  Law,  45. 
Bunsen  cell,  323. 


Calorie,  100,  101. 

Calorimetry,  102. 

Camera,  pin-hoie,  195. 

Capillary  action,  1 7. 

Cause,  128. 

Center  of  curvature,  206,  220 ;    of 

gravity,   266;     of    suspension, 

157 ;  optical,  220. 
Circuit,  divided,  348. 
Charles,  Law  of,  92. 
Chemical  action  in  cells,  336,  340. 
Coefficient  of  friction,  277,  279 ;  of 

linear  expansion,  88. 
Coercive  force,  322. 
Commutator,  342. 
Concord,  176. 

Condensation  explained,  130. 
Conduction  of  heat,  97. 
Conjugate  foci,  226. 
Conservation  of  energy,  302. 
Convection,  97. 
Couple,  255  ;  arm  of,  255. 
Current,  electric,  325;     action  on 

magnets  of,  327 ;    strength  of, 

327. 

Dalton,  92 ;  Law  of,  94,  95. 
Daniell  cell,  323. 
Density,  7. 
Dew-point,  124. 

Directions  for  note-taking,  1 ;    for 
performing  experiments,  2. 


376 


INDEX. 


Discord,  176. 
Dynamics,  245. 
Dyne,  298. 

Elasticity,  limits  of,  141 ;  of  bend- 
ing, 142 ;  of  stretching,  138 ;  of 
shape,  141 ;  of  twisting,  147 ; 
of  volume,  151. 

Electric  current,  325. 

Electro-magnetism,  363. 

Electro-motive  force,  352. 

Energy,  301 ;  conservation  of,  302 ; 
kinetic,  302 ;  potential,  302. 

Equilibrium,  249;  of  concurrent 
forces,  273 ;  of  parallel  forces, 
249,  261. 

Equipotential  points,  369. 

Erg,  299. 

Ether,  241. 

Evaporation,  121;  explained,  130. 

Exhaustion,  degree  of,  41. 

Expansion,  cubical,  85;  linear,  85; 
of  air,  90. 

Experience,  62. 

Experiment,  62;  qualitative,  63; 
quantitative,  63. 

Facts  and  inferences,  63. 

Fixed  points,  74. 

Fluid,  130. 

Focal  length,  223. 

Foci,  conjugate,  226. 

Focus,  principal,  221. 

Foot-pound,  281 ;  -poundal,  301. 

Force,  141 ;  components  of  a,  276 ; 
of  friction,  276  ;  line  of,  316; 
moment  of  a,  260 ;  transverse, 
144 ;  units  of,  246,  298,  300. 

Forces,  composition  of,  276 ;  con- 
current, 271 ;  equilibrant  of 
concurrent,  274;  resultant  of 


concurrent,  274;  representa- 
tion of,  247 ;  resolution  of, 
276;  triangle  of,  273. 

Freezing  mixtures,  117  ;  point,  74. 

Friction,  276. 

Fulcrum,  270. 

Fusion,  latent  heat  of,  112. 

Galvanometer,  tangent,  366 ;  astat- 
ic, 366. 

Galvanoscope,  335. 
Gay-Lussac,  84,  92. 
Gram,  8,  301. 
Graphical  method,  59. 
Gravity,  265 ;  center  of,  266. 

Heat,  75 ;  conduction  of,  97 ;  con- 
vection of,  97;  latent,  109; 
measurement  of,  100 ;  mechan- 
ical equivalent  of,  304;  of  fu- 
sion, 112  ;  of  vaporization,  117  ; 
radiation  of,  97;  sensible,  110; 
specific,  106 ;  unit  of,  100,  101. 

Helmholtz,  182. 

Hiero,  12. 

Hooke's  Law,  152. 

Hydrostatic  press,  55. 

Hypothesis,  129;  molecular,  129. 

Illumination,  intensity  of,  188. 

Images,  construction  for  real,  233 ; 
for  virtual,  238 ;  formation  of, 
by  small  apertures,  194,  by 
cylindrical  mirrors,  208,  209, 
by  lenses,  222,  235,  -by  plane 
mirrors,  198 ;  number  of,  204 ; 
real,  201;  virtual,  201. 

Inclined  plane,  285. 

Index  of  refraction,  216. 

Inertia,  286. 

Inferences,  63. 


INDEX. 


377 


Interference  of  light,  242;  of 
sound,  167. 

Jevons,  W.  Stanley,  127,  129. 
Joule,  304. 

Kaleidoscope,  204. 
Kinetic  energy,  302. 
Kinetics,  245. 

Knowledge,  classified,  128 ;  empiri- 
cal, 127. 

Lagrange,  182. 

Latent  heat,  109;  of  fusion,  112; 
of  vaporization,  117. 

Laws  of  nature,  183. 

Lenses,  220 ;  definitions  relating  to, 
220 ;  names  and  properties  of, 
221,  222 ;  focal  length  of,  223  ; 
relation  of,  to  prisms,  219. 

Levers,  classes  of,  270 ;  influence 
of  weight  of,  266 ;  law  of,  271. 

Light,  beam  of,  192  ;  interference 
of,  242 ;  nature  of,  240 ;  pencil 
of,  192;  rays  of,  192  ;  reflection 
of,  196;  refraction  of,  211, 123 ; 
velocity  of,  240. 

Liquid  pressure,  24. 

Lodestones,  313. 

Lucretius,  129. 

Magnets,  action  of  currents  on, 
327  ;  poles  of,  309. 

Magnetic  attractions  and  repul- 
sions, 311;  compass,  312; 
curves,  316  ;  field,  316  ;  force, 
line  of,  316;  induction,  314; 
needle,  312. 

Magnetism,  theory  of,  321. 

Magnetite,  313. 

Magnifying  glass,  240. 


Mariotte's  bottle,  57. 

Mass,  245 ;  unit  of,  246. 

Maxwell,  J.  Clerk,  130. 

Measurements  and  computations,  8. 

Mechanical  equivalent  of  heat,  304. 

Mersenne,  182. 

Method,  bridge,  369;  graphical,  59 ; 
of  differences,  127 ;  of  mix- 
tures, 102 ;  of  substitution,  368. 

Mirrors,  cylindrical,  205;  plane,  198. 

Molecule,  129. 

Moment  of  a  force,  259,  260. 

Momentum,  292. 

Newton,  241. 

Note-taking,  directions  for,  1. 

Numerical  value,  5. 

Observation,  62 ;  fallacies  of,  184. 
Octave,  176. 
Ohm,  the,  350. 
Ohm's  Law,  352. 
Optical  center,  220. 
Oscillation,  157. 

Parallax,  227. 

Pendulum,  157 ;  length  of,  158. 

Penumbra,  194. 

Photometry,  192. 

Pitch,  180. 

Pneumatics,  23. 

Poggendorff  cell,  341. 

Polarization,  337. 

Potential,  369. 

Pound,  246. 

Poundal,  300. 

Prisms  and  lenses,  219. 

Pump,  air,  48 ;  force,  51 ;  lifting,  50. 

Pythagoras,  181. 

Quality  of  sounds,  180. 
Quantity,  5. 


378 


INDEX. 


Radiation  of  heat,  97. 
Reflection  of  light,  196. 
Refraction,  index  of,  216 ;  of  light, 

211,  214. 

Residual  magnetism,  322. 
Resistance  battery,  353 ;  external, 

353;  internal,  353;  of  wires,  343. 
Retentivity,  322. 
Rheostat,  342. 
Rotation,  negative,  260;  positive, 

260. 
Rudberg,  85. 

Shadows,  193. 

Shore,  John,  164. 

Siphon,  53. 

Soldering,  139. 

Sound,  interference  of,  167 ;  loud- 
ness  of,  180 ;  pitch,  180 ;  trans- 
mission of,  165;  theory  of, 
181 ;  velocity  of,  161 ;  quality 
of,  180 ;  wave,  form  of,  168. 

Sound  radiometer,  174. 

Specific  gravity,  11 ;  and  density, 
19 ;  of  air,  38 ;  of  a  liquid,  18, 
35 ;  of  a  solid,  15,  19. 

Specific  heat,  106. 

Statics,  245. 

Steam  engine,  305. 

Strain  and  stress,  151. 

Sympathetic  vibrations,  174. 

Temperature,  75 ;  absolute  94 ;  and 
pressure,  75 ;  and  resistance, 
373. 


Temporary  magnetism,  322. 
Theory,  184. 
Thermal  capacity,  102. 
Thermometer,  air,  93 ;  mercury,  71. 
Torricelli,  31 ;  experiment  of,  31. 
Triangle  of  forces,  273. 
Tuning-fork,  164. 

Umbra,  194. 
Unit,  7. 

Units,  absolute,  300;  gravitation, 
300. 

Vapor,  saturated,  131. 

Velocity,  288;    of  light,   240;    of 

sound,  161,  172. 
Vibration,  157 ;  of  strings,  176. 
Volt,  the,  352. 

Water,  boiling-point  of,  79 ;  freez- 
ing-point of,  74;  maximum 
density  of,  125. 

Wave  crest,  156;  length,  156;  mo- 
tion, 155;  motion  of  sound, 
166;  trough,  156. 

Weight,  247. 

Wheatstone's  bridge,  369;  theory 
of,  371. 

Wollaston,  185. 

Work,  280. 

Zero,  absolute,  94;  error  of  bal- 
ance, 5. 

Zero-point,  elevation  of,  83 ;  lower- 
ing of,  83. 


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